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CBSE 10th Standard Maths Subject Coordinate Geometry Case Study Questions 2021
By QB365 on 22 May, 2021
QB365 Provides the updated CASE Study Questions for Class 10 Maths, and also provide the detail solution for each and every case study questions . Case study questions are latest updated question pattern from NCERT, QB365 will helps to get more marks in Exams
QB365 - Question Bank Software
10th Standard CBSE
Final Semester - June 2015
Case Study Questions
(ii) How far is the library from Shaguns house?
(iii) How far is the library from Alia's house?
(iv) Which of the following is true?
(v) How far is the school from Alia's house than Shaguns house?
| units | units | + )units | - ) units |
(ii) The value of x is equal to
(iii) If M is any point exactly in between city A and city B, then coordinates of M are
(iv) The ratio in which A divides the line segment joining the points O and M is
(v) If the person analyse the petrol at the point M(the mid point of AB), then what should be his decision?
(ii) The distance of the bus stand from the house is
(iii) If the grocery store and electrician's shop lie on a line, the ratio of distance of house from grocery store to that from electrician's shop, is
(iv) The ratio of distances of house from bus stand to food cart is
(v) The coordinates of positions of bus stand, grocery store, food cart and electrician's shop form a
| d) none of these |
| \(A\left(\frac{2}{3}, 0\right),\) | \((b) \left(0, \frac{2}{3}\right)\) | \((c) \left(0, \frac{4}{3}\right)\) | \((d) \left(\frac{4}{3}, 0\right)\) |
(ii) The centre of circle is the
(iii) The radius of the circle is
| \((a) \frac{4}{3} units\) | \((b) \frac{3}{2} units\) | \((c) \frac{2}{3} units\) | \((d) \frac{3}{4} units\) |
(iv) The area of the circle is
| \((a) 16 \pi^{2} sq. units\) | \((b) \frac{16}{9} \pi sq. units\) | \((c) \frac{4}{9} \pi^{2} sq. units\) | \((d) 4 \pi sq. units\) |
(v) If \(\left(1, \frac{\sqrt{7}}{3}\right)\) is one of the ends of a diameter, then its other end is
| \((a) \left(-1, \frac{\sqrt{7}}{3}\right)\) | \((b) \left(1,-\frac{\sqrt{7}}{3}\right)\) | \((c) \left(1, \frac{\sqrt{7}}{3}\right)\) | \((d) \left(-1,-\frac{\sqrt{7}}{3}\right)\) |
| \((a) \left(\frac{2}{3}, \frac{7}{3}\right)^{n}\) | \((b) \left(\frac{1}{3}, \frac{1}{3}\right)\) | \((c) \left(\frac{-2}{3}, \frac{7}{3}\right)\) | \((d) \left(\frac{7}{3}, \frac{2}{3}\right)\) |
(ii) If S be the mid-point of line joining P and Q, then coordinates of S are
(iii) If T be the mid-point of line joining Rand Q, then coordinates of T are
| \((a) \left(\frac{1}{2}, \frac{1}{2}\right)\) | \((b) \left(\frac{3}{2}, \frac{1}{2}\right)\) | \((c) \left(\frac{1}{2}, \frac{3}{2}\right)\) |
(iv) If Ube the mid-point of line joining Rand P, then coordinates of U are
| \((a) \left(-\frac{5}{2}, \frac{3}{2}\right)\) | \((b) \left(\frac{3}{2},-\frac{5}{2}\right)\) | \((c) \left(\frac{3}{2}, \frac{5}{2}\right)\) | \((d) \left(\frac{5}{2}, \frac{3}{2}\right)\) |
(v) The coordinates of centroid of \(\Delta\) STU are
| \((a) \left(\frac{2}{3}, \frac{7}{3}\right)\) | \((b) \left(\frac{1}{3}, \frac{1}{3}\right)\) | \((c) \left(-\frac{2}{3}, \frac{7}{3}\right)\) | \((d) \left(\frac{7}{3}, \frac{2}{3}\right)\) |
*****************************************
Cbse 10th standard maths subject coordinate geometry case study questions 2021 answer keys.
(i) (d): Since the coordinates of A and Bare (2, 3) and (2, 1) respectively. \(\therefore\) Required distance = AB \(=\sqrt{(2-2)^{2}+(1-3)^{2}}=\sqrt{2^{2}}=2 \text { units }\) (ii) (b): Since, library is situated at C(4, 1) \(\therefore\) Required distance = BC \(=\sqrt{(4-2)^{2}+(1-1)^{2}}=\sqrt{2^{2}+0^{2}}=2 \text { units }\) (iii) (d): Required distance = AC \(=\sqrt{(4-2)^{2}+(1-3)^{2}}=\sqrt{2^{2}+2^{2}}=2 \sqrt{2} \text { units }\) (iv) (b): Since AB = BC \(\neq\) AC, therefore \(\Delta\) ABC is an isosceles triangle. (v) (d): Distance between O and A \(=\sqrt{2^{2}+3^{2}}=\sqrt{4+9}=\sqrt{13} \text { units }\) and distance between O and B = \(\sqrt{2^{2}+1^{2}}=\sqrt{4+1}=\sqrt{5} \text { units }\) Thus, required distance = \((\sqrt{13}-\sqrt{5}) \text { units }\)
(i) (a): We have, OA = 2 \(\sqrt{2}\) km \(\Rightarrow \sqrt{2^{2}+y^{2}}=2 \sqrt{2} \) \(\Rightarrow 4+y^{2}=8 \Rightarrow y^{2}=4 \) \(\Rightarrow y=2 \quad(\because y=-2 \text { is not possible })\) (ii) (c): We have OB = 8 \(\sqrt{2}\) \(\Rightarrow \sqrt{x^{2}+8^{2}}=8 \sqrt{2} \) \(\Rightarrow x^{2}+64=128 \Rightarrow x^{2}=64 \) \(\Rightarrow x=8 \quad(\because x=-8 \text { is not possible })\) (iii) (c) : Coordinates of A and Bare (2, 2) and (8, 8) respectively, therefore coordinates of point M are \(\left(\frac{2+8}{2}, \frac{2+8}{2}\right)\) i.e .,(5.5) (iv) (d): Let A divides OM in the ratio k: 1.Then \(2=\frac{5 k+0}{k+1} \Rightarrow 2 \mathrm{k}+2=5 k \Rightarrow 3 k=2 \Rightarrow k=\frac{2}{3}\) \(\therefore\) Required ratio = 2 : 3 (v) (b): Since M is the mid-point of A and B therefore AM = MB. Hence, he should try his luck moving towards B.
(i) (c): Required coordinates are \(\left(0, \frac{4}{3}\right)\) (ii) (c) (iii) (a): Radius = Distance between (0,0) and \(\left(\frac{4}{3}, 0\right)\) \(=\sqrt{\left(\frac{4}{3}\right)^{2}+0^{2}}=\frac{4}{3} \text { units }\) (iv) (b): Area of circle = \(\pi\) (radius) 2 \(=\pi\left(\frac{4}{3}\right)^{2}=\frac{16}{9} \pi \text { sq. units }\) (v) (d): Let the coordinates of the other end be (x,y). Then (0,0) will bethe mid-point of \(\left(1, \frac{\sqrt{7}}{3}\right)\) and (x, y). \(\therefore\left(\frac{1+x}{2}, \frac{\frac{\sqrt{7}}{3}+y}{2}\right)=(0,0) \) \(\Rightarrow \frac{1+x}{2}=0 \text { and } \frac{\frac{\sqrt{7}}{3}+y}{2}=0 \) \(\Rightarrow x=-1 \text { and } y=-\frac{\sqrt{7}}{3}\) Thus, the coordinates of other end be \(\left(-1, \frac{-\sqrt{7}}{3}\right)\)
(i) (c): We have, P( -3,4), Q(3, 4) and R( -2, -1). \(\therefore\) Coordinates of centroid of \(\Delta\) PQR \(=\left(\frac{-3+3-2}{3}, \frac{4+4-1}{3}\right)=\left(\frac{-2}{3}, \frac{7}{3}\right)\) (ii) (d): Coordinates of S= \(\left(\frac{-3+3}{2}, \frac{4+4}{2}\right)=(0,4)\) (iii) (c): Coordinates of T= \(\left(\frac{-2+3}{2}, \frac{-1+4}{2}\right)=\left(\frac{1}{2}, \frac{3}{2}\right)\) (iv) (a): Coordinates of U = \(\left(\frac{-2-3}{2}, \frac{-1+4}{2}\right)=\left(\frac{-5}{2}, \frac{3}{2}\right)\) (v) (c): The centroid of triangle formed by joining the mid-points of sides of given triangle is same as that of the given trangle. So, centroid of \(\Delta S T U=\left(\frac{-2}{3}, \frac{7}{3}\right)\)
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CBSE Class 10 Maths Case Study Questions for Chapter 7 - Coordinate Geometry (Released By CBSE)
Cbse's question bank on case study for class 10 maths chapter 7 is available here. practice this new type of questions to score good marks in your board exam..
Case study based questions for CBSE Class 10 Maths Chapter 7 - Coordinate Geometry are provided here for students to practice this new format of questions for their Maths Board Exam 2022. All these questions are published by the Central Board of Secondary Education (CBSE) for Class 10 Maths. Students must solve these questions to familiarise themselves with the concepts and logic used in the case study. You can also check the right answer at the end of each question.
Check Case Study Questions for Class 10 Maths Chapter 7 - Coordinate Geometry
CASE STUDY 1:
In order to conduct Sports Day activities in your School, lines have been drawn with chalk powder at a distance of 1 m each, in a rectangular shaped ground ABCD, 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in given figure below. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5th distance AD on the eighth line and posts a red flag.
1. Find the position of green flag
b) (2,0.25)
d) (0, -25)
Answer: a) (2,25)
2. Find the position of red flag
Answer: c) (8,20)
3. What is the distance between both the flags?
a) √41
b) √11
c) √61
d) √51
Answer: c) √61
4. If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?
a) (5, 22.5)
d) (2.5,20)
Answer: a) (5, 22.5)
5. If Joy has to post a flag at one-fourth distance from green flag , in the line segment joining the green and red flags, then where should he post his flag?
a) (3.5,24)
b) (0.5,12.5)
c) (2.25,8.5)
Answer: a) (3.5,24)
CASE STUDY 2:
The class X students school in krishnagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is triangular grassy lawn in the plot as shown in the figure. The students are to sow seeds of flowering plants on the remaining area of the plot.
1. Taking A as origin, find the coordinates of P
Answer: a) (4,6)
2. What will be the coordinates of R, if C is the origin?
Answer: c) (10,3)
3. What will be the coordinates of Q, if C is the origin?
b) b) (-6,13)
Answer: d) (13,6)
4. Calculate the area of the triangles if A is the origin
Answer: a) 4.5
5. Calculate the area of the triangles if C is the origin
Answer: d) 4.5
Also Check:
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CBSE Class 10 Maths Best Study Material for 2021-2022
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CBSE Case Study Questions for Class 10 Maths Coordinate Geometry Free PDF
Mere Bacchon, you must practice the CBSE Case Study Questions Class 10 Maths Coordinate Geometry in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!
I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams. To download the latest CBSE Case Study Questions , just click ‘ Download PDF ’.
CBSE Case Study Questions for Class 10 Maths Coordinate Geometry PDF
Mcq set 1 -, mcq set 2 -, checkout our case study questions for other chapters.
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CBSE Class 10 Maths Case Study Questions PDF
Download Case Study Questions for Class 10 Mathematics to prepare for the upcoming CBSE Class 10 Final Exam. These Case Study and Passage Based questions are published by the experts of CBSE Experts for the students of CBSE Class 10 so that they can score 100% on Boards.
CBSE Class 10 Mathematics Exam 2024 will have a set of questions based on case studies in the form of MCQs. The CBSE Class 10 Mathematics Question Bank on Case Studies, provided in this article, can be very helpful to understand the new format of questions. Share this link with your friends.
Table of Contents
Chapterwise Case Study Questions for Class 10 Mathematics
Inboard exams, students will find the questions based on assertion and reasoning. Also, there will be a few questions based on case studies. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.
The above Case studies for Class 10 Maths will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 10 Mathematics Case Studies have been developed by experienced teachers of cbseexpert.com for the benefit of Class 10 students.
- Class 10th Science Case Study Questions
- Assertion and Reason Questions of Class 10th Science
- Assertion and Reason Questions of Class 10th Social Science
Class 10 Maths Syllabus 2024
Chapter-1 real numbers.
Starting with an introduction to real numbers, properties of real numbers, Euclid’s division lemma, fundamentals of arithmetic, Euclid’s division algorithm, revisiting irrational numbers, revisiting rational numbers and their decimal expansions followed by a bunch of problems for a thorough and better understanding.
Chapter-2 Polynomials
This chapter is quite important and marks securing topics in the syllabus. As this chapter is repeated almost every year, students find this a very easy and simple subject to understand. Topics like the geometrical meaning of the zeroes of a polynomial, the relationship between zeroes and coefficients of a polynomial, division algorithm for polynomials followed with exercises and solved examples for thorough understanding.
Chapter-3 Pair of Linear Equations in Two Variables
This chapter is very intriguing and the topics covered here are explained very clearly and perfectly using examples and exercises for each topic. Starting with the introduction, pair of linear equations in two variables, graphical method of solution of a pair of linear equations, algebraic methods of solving a pair of linear equations, substitution method, elimination method, cross-multiplication method, equations reducible to a pair of linear equations in two variables, etc are a few topics that are discussed in this chapter.
Chapter-4 Quadratic Equations
The Quadratic Equations chapter is a very important and high priority subject in terms of examination, and securing as well as the problems are very simple and easy. Problems like finding the value of X from a given equation, comparing and solving two equations to find X, Y values, proving the given equation is quadratic or not by knowing the highest power, from the given statement deriving the required quadratic equation, etc are few topics covered in this chapter and also an ample set of problems are provided for better practice purposes.
Chapter-5 Arithmetic Progressions
This chapter is another interesting and simpler topic where the problems here are mostly based on a single formula and the rest are derivations of the original one. Beginning with a basic brief introduction, definitions of arithmetic progressions, nth term of an AP, the sum of first n terms of an AP are a few important and priority topics covered under this chapter. Apart from that, there are many problems and exercises followed with each topic for good understanding.
Chapter-6 Triangles
This chapter Triangle is an interesting and easy chapter and students often like this very much and a securing unit as well. Here beginning with the introduction to triangles followed by other topics like similar figures, the similarity of triangles, criteria for similarity of triangles, areas of similar triangles, Pythagoras theorem, along with a page summary for revision purposes are discussed in this chapter with examples and exercises for practice purposes.
Chapter-7 Coordinate Geometry
Here starting with a general introduction, distance formula, section formula, area of the triangle are a few topics covered in this chapter followed with examples and exercises for better and thorough practice purposes.
Chapter-8 Introduction to Trigonometry
As trigonometry is a very important and vast subject, this topic is divided into two parts where one chapter is Introduction to Trigonometry and another part is Applications of Trigonometry. This Introduction to Trigonometry chapter is started with a general introduction, trigonometric ratios, trigonometric ratios of some specific angles, trigonometric ratios of complementary angles, trigonometric identities, etc are a few important topics covered in this chapter.
Chapter-9 Applications of Trigonometry
This chapter is the continuation of the previous chapter, where the various modeled applications are discussed here with examples and exercises for better understanding. Topics like heights and distances are covered here and at the end, a summary is provided with all the important and frequently used formulas used in this chapter for solving the problems.
Chapter-10 Circle
Beginning with the introduction to circles, tangent to a circle, several tangents from a point on a circle are some of the important topics covered in this chapter. This chapter being practical, there are an ample number of problems and solved examples for better understanding and practice purposes.
Chapter-11 Constructions
This chapter has more practical problems than theory-based definitions. Beginning with a general introduction to constructions, tools used, etc, the topics like division of a line segment, construction of tangents to a circle, and followed with few solved examples that help in solving the exercises provided after each topic.
Chapter-12 Areas related to Circles
This chapter problem is exclusively formula based wherein topics like perimeter and area of a circle- A Review, areas of sector and segment of a circle, areas of combinations of plane figures, and a page summary is provided just as a revision of the topics and formulas covered in the entire chapter and also there are many exercises and solved examples for practice purposes.
Chapter-13 Surface Areas and Volumes
Starting with the introduction, the surface area of a combination of solids, the volume of a combination of solids, conversion of solid from one shape to another, frustum of a cone, etc are to name a few topics explained in detail provided with a set of examples for a better comprehension of the concepts.
Chapter-14 Statistics
In this chapter starting with an introduction, topics like mean of grouped data, mode of grouped data, a median of grouped, graphical representation of cumulative frequency distribution are explained in detail with exercises for practice purposes. This chapter being a simple and easy subject, securing the marks is not difficult for students.
Chapter-15 Probability
Probability is another simple and important chapter in examination point of view and as seeking knowledge purposes as well. Beginning with an introduction to probability, an important topic called A theoretical approach is explained here. Since this chapter is one of the smallest in the syllabus and problems are also quite easy, students often like this chapter
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Case Study Questions for Class 10 Maths Chapter 7 Coordinate Geometry
- Last modified on: 1 year ago
- Reading Time: 3 Minutes
Case Study Questions:
Question 1:
The top of a table is shown in the figure given below:
(i) The coordinates of the points H and G are respectively (a) (1, 5), (5, 1) (b) (0, 5), (5, 0) (c) (1, 5), (5, 0) (d) (5, 1), (1, 5)
(ii) The distance between the points A and B is (a) 4 units (b) 4 2 units (c) 16 units (d) 32 units
(iii) The coordinates of the mid point of line segment joining points M and Q are (a) (9, 3) (b) (5, 11) (c) (14, 14) (d) (7, 7)
(iv) Which among the following have same ordinate? (a) H and A (b) T and O (c) R and M (d) N and R
(v) If G is taken as the origin, and x, y axis put along GF and GB, then the point denoted by coordinate (4, 2) is (a) H (b) F (c) Q (d) R
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You may also like:
Chapter 1 Real Numbers Chapter 2 Polynomials Chapter 3 Pair of Linear Equations in Two Variables C hapter 4 Quadratic Equations Chapter 5 Arithmetic Progressions Chapter 6 Triangles Chapter 7 Coordinate Geometry Chapter 8 Introduction to Trigonometry Chapter 9 Some Applications of Trigonometry Chapter 10 Circles Chapter 11 Constructions Chapter 12 Areas Related to Circles Chapter 13 Surface Areas and Volumes Chapter 14 Statistics Chapter 15 Probability
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Class 10 Maths Chapter 7 Case Based Questions - Coordinate Geometry
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Study Case - 1
The class X students of a school in Rajinder Nagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Mango are planted on the boundary at the distance of 1 m from each other.
Based on the above figure, answer the following questions:
Q4: What will be the coordinates of the vertices of ΔPQR if C is the origin? (a) (14, 3), (11, 2), (8, 6) (b) (15, 4), (12, 3), (9, 7) (c) (14, 2), (11, 1), (8, 5) (d) (15, 3), (12, 2), (9, 6) Ans: (d) Explanation: When C is taken as origin, we will take CB as X-axis and CD as Y-axis. Then, coordinates of points, P, Q and R are (15, 3), (12, 2)and (9, 6) respectively.
Q5: What are the coordinates of P if D is taken as the origin? (a) (−15, 5) (b) (15, 5) (c) (15, 7) (d) (15, 3) Ans: (a) Explanation: When D is taken as origin, we will take DA as negative X-axis and DC as positive Y-axis. Then coordinates of point P is (−15, 5).
Case Study - 2
Based on the above information, give the answer of the following questions:
Study Case - 3
Based on the above information give the answer of the following questions:
Q1: The coordinates of the point A are: (a) (4,9) (b) (5,9) (c) (92,9) (d) (4,8) Ans: (c) Explanation: As the distance of point A is 9/2 units from the Y-axis and 9 units from the X-axis, its coordinates are x = 9/2, y = 9 or (9/2, 9)
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CBSE Class 10 Maths Important Questions on Chapter 7 - Coordinate Geometry
- Class 10 Important Question
- Chapter 7: Coordinate Geometry
CBSE Class 10 Maths Important Questions Chapter 7 - Coordinate Geometry - Free PDF Download
Vedantu has provided the important questions for CBSE Class 10 Maths Chapter 7 - Coordinate Geometry in a manner that students will find easy to understand and study. Our expert teachers have spent dutiful hours in making these questions as close to the ones in the actual paper as possible. Students will most likely find these questions common in their question paper since we follow the CBSE guidelines strictly in this regard. This chapter introduces students to coordinate geometry in mathematics. Mathematics is known to be a tough subject and this article is supposed to help students to figure out how to study the important topics in the chapter by going over the important questions that are provided in Vedantu. This article shows students how to prepare for any upcoming examinations by helping them practise the sums that are relevant and have a higher chance of coming into the exam. Mathematics is a complex subject to study on your own and to help students can use important questions of coordinate geometry class 10 provided to ace their examinations. Class 10 boards are very important for students and to help prepare and do well they can do the questions as a part of their revision.
Vedantu is a platform that provides free NCERT Book Solutions and other study materials for students. You can Download Maths NCERT Solutions Class 10 and NCERT Solution Class 10 Science to help you to revise the complete Syllabus and score more marks in your examinations.
Download CBSE Class 10 Maths Important Questions 2024-25 PDF
Also, check CBSE Class 10 Maths Important Questions for other chapters:
CBSE Class 10 Maths Important Questions | ||
Sl.No | Chapter No | Chapter Name |
1 | Chapter 1 |
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2 | Chapter 2 |
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3 | Chapter 3 |
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4 | Chapter 4 |
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5 | Chapter 5 |
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6 | Chapter 6 |
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7 | Chapter 7 | Coordinate Geometry |
8 | Chapter 8 |
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9 | Chapter 9 |
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10 | Chapter 10 |
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11 | Chapter 11 |
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12 | Chapter 12 |
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13 | Chapter 13 |
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14 | Chapter 14 |
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15 | Chapter 15 |
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Related Chapters
Chapter 7 Maths Class 10 Important Questions- Free PDF Download
Students looking to find important questions for coordinate geometry can find it here in this article at the Vedantu website which is free and easily available for the student. The website allows for easy access to its important questions and also it is easily downloadable. Students will find these notes to be helpful during the preparation of their examinations, these important questions are easily downloadable in a pdf format. Students who find it difficult to study on the screen can also print this material so they don't waste too much time on the internet. These questions can come for more marks than what is anticipated and so students need to be thorough with their preparation. Class 10 board examination is an important one for students and students need to know how to prepare well for it so they can do well because the marks they score in 10th will carry on for life long. So students need to prepare early and have continuous revisions and to help them with that they can use this article which will help guide them through this chapter on coordinate geometry.
Important Topics Covered under CBSE Class 10 Maths Chapter 7 - Coordinate Geometry
Coordinate geometry draws the linkage between geometry and algebra using various graphs and lines. Some of the concepts covered in this chapter are as follows
History of Coordinate Geometry
Coordinate geometry was first introduced by a French mathematician known as Rene Descartes; he was the first person to find a method to describe the location of points. Later in his research, he concluded that different curves and lines could be found using equations using coordinate geometry. He was the first person to draw the link between geometry and algebra. His work was considered extremely useful and to honour his work the coordinates of a point are called cartesian coordinates and the coordinate plane is known as the cartesian coordinate plane.
Coordinates
Coordinates are simply the various points on the plane. Using the x-axis and y-axis we can find out the exact location of the point. Because we are using a grid system it is much easier to locate anything because we just need to identify which cell( the intersection of rows and columns) the point falls.
Coordinate Plane
In coordinate geometry, there is a coordinate plane where different points are placed. There are usually two different scales- one with right angles to it is known as the y axis and the one running across from the plane is known as the x-axis. The point of origin is where both the x and y-axis meet and are known as the point of origin, this is usually at point 0.
Co coordinate geometry is quite simple, it uses pairs of numbers to give the location of a point on a plane.
Advantages of Coordinate Geometry
When we know the coordinates of certain points we can do the following- Determine the distance between them
We can find the equation, slope, and midpoint of any line segment.
We can find whether the lines are perpendicular or parallel.
Using the points we can find the perimeter and areas of any polygon.
By Reflecting, moving, and rotating we can transform any shape.
Define various eclipses, curves, and circles.
Find out the distances between different points, lines, and shapes.
Class 10 Maths Chapter 7 Important Questions
This chapter introduces students to coordinate geometry and students can study from this subject the very basics and get to a more intermediate level. The following are the important questions that students must look at when preparing for their examinations-
There are two routes to use to travel from destination A to destination B. First Bus reaches via point C and the second bus reaches from A to B Directly. If Coordinates of A, B, and C are (-2,-3),(2,3), and (3,2) respectively then which bus do you want to travel from A to B? which value is depicted in the question.
On a sports day celebration, Shyam and Ram are standing at positions A and B and their coordinates are (2,-2) and (4,8). The teachers ask Pooja to fix the flag at the midpoint of the line joining points A and B. Find the coordinates of the midpoint? Which type of value would you infer from the question?
To raise awareness of the hazard of smoking and the harm it does to the body, a school decided to start a “ no smoking” campaign. 10 students are asked to prepare campaign flags in the shape of a triangle. If the costs of 1cm2 of each banner are 2 rupees then find the overall cost incurred in the campaign. Which value is depicted in the question?
Find the area of a rhombus if its vertices are (3,0), (4,5),(-1,4) and (-2,-1) taken in the area.
Find the centroid of a triangle whose vertices are(4,-8), (-9,7), and (8, 13).
Prove that in a right-angled triangle the midpoint of the hypotenuse is in equal distance from all its vertices
Prove that the diagonals of a rectangle bisect each other are all equal.
The length of a line segment is 10. If one endpoint (2,-3) and the abscissa of the second endpoint is 10 shows that the ordinate is 3 or -9.
Using section formulas show that points (-1,2),(5,0) and (2,1) are collinear.
Find the relation between x and y such that point (x,y) is equidistant from the points (7,1) and (3,5).
Some Practice Questions on CBSE Class 10 Maths Chapter 7 - Coordinate Geometry
(2a, a – 7) is the centre of a given circle. If the circle is passing through the point (11, –9) and it has a diameter of 10√2 units, then determine the value of a.
Are the points (1, 7), (4, 2), (–1, –1), and (– 4, 4) the vertices of a square? Explain why.
Determine a point on the x-axis that is equidistant from (2, –5) and (–2, 9).
Determine the ratio in which the line segment joining the points (8, –9) and (2, 1) is divided into by the line 2x + 3y – 5 = 0. Also, determine the coordinates of this point of division.
If the vertices of a rhombus are (3, 0), (4, 5), (– 1, 4), and (– 2, – 1), when taken in order, then determine its area. [ Hint : Area of a rhombus = 1/2 (product of its diagonals)]
The distances of P(x, y) from A(5, 1) and B(-1, 5) are equal. Prove that 3x = 2y.
What ratio is the line segment joining the points P(2, -2) and Q(3, 7) divided by the point (24/11, y)? Also, determine the value of y.
The points A (1, –2), B (2, 3) C (a, 2) and D (– 4, –3) form a parallelogram. Determine the value of a and the height of this parallelogram, by considering AB to be the base.
The vertices of a triangle are (1, -1), (-4, 6), and (-3, -5). Determine its area.
The points A(x, y), B(-4, 6), and C(-2, 3) are collinear. Find a relation between x and y.
Benefits of Class 10 Maths Chapter 7 Important Questions
Mathematics can be quite a difficult subject to understand by yourself. So by using the right guide material like the ones found in Vedantu students can utilise it to their maximum and score the best marks possible. A lot of this subject is a theory so students need to just understand the various concepts and don't have to mug up anything like science subjects.
Students can use this text to use their time wisely, it helps boost their confidence after consistent practice and students can plan their preparation accordingly.
Students can utilise and practise the important questions so that they can ace their examinations.
It provides students with a structure with which they will study for his or her upcoming examinations.
This is a fundamental subject for high school kids and plays an important role in higher studies.
Students don’t need to worry about the relevance of these questions as they're all cross-checked and updated consistently with the newest CBSE guidelines and rules. Therefore, the information in Vedantu is genuine and reliable.
Students studying this chapter on coordinate geometry will find that it helps in higher studies and helps them understand the basics in any design engineering field.
Conclusion
Mathematics is known to be a difficult subject. Coordinates are simply the various points on a plane. Using the x-axis and y-axis we can find out the exact location of the point. students will learn how to use various coordinate plans and different ways to locate points, lines, curves, and shapes. Students can use this article to use their time wisely, it helps boost their confidence after consistent practice and students can plan their preparation accordingly. Students can work more diligently towards their goals and strive for higher marks as well. These important questions make sure that students are aware of the various topics in the subject and learn to master all the concepts. This chapter teaches students to coordinate geometry in mathematics the questions provided in this article helps students understand the subject better.
Important Related Links for CBSE Class 10 Maths
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FAQs on CBSE Class 10 Maths Important Questions on Chapter 7 - Coordinate Geometry
1. What does Class 10 Maths Chapter 7 depict?
Class 10 Maths Chapter 7 depicts Coordinate Geometry which is the branch of Mathematics. It helps us to exactly locate a given point with the help of an ordered pair of numbers.
Coordinate geometry is also well known as Cartesian Geometry. It helps in finding the distance between two points whose coordinates are given. The coordinates of the point can also be found by this theory, which divides the line segment joining two points in the given ratio. Through this, you can also learn how to find the area of a triangle with reference to the coordinate of its vertices.
2. What is Coordinate Geometry?
Coordinate Geometry is considered to be one of the most interesting chapters of Mathematics. Coordinate Geometry (or the analytic geometry) depicts the link between Geometry and Algebra through graphs that involve curves and lines.
Coordinate geometry is named as the study of graphs. Graphs are the visual representations of the data that derives from every aspect of our lives. There are various types of graphs like bar graphs, histograms, line graphs, etc.
3. Why should I opt for Important Questions for Class 10 Maths Chapter 7?
As the name suggests, Important Questions for Class 10 Maths Chapter 7 is the compilation of all the important questions from the specified chapter. These questions are truly important for all the students who are preparing for the board exam and eager to score the best possible marks in the exam. This questionnaire is created on the basis of previous years question papers, textbook exercises, chapter-wise weightage etc.
4. Can I download the solutions of these Important Questions for Class 10 Maths Chapter 7?
Yes, you can download the solutions of these Important Questions for Class 10 Maths Chapter 7 titled Coordinate Geometry from Vedantu website (vedantu.com). These solutions are created by our in-house experts hence you will not have to doubt its accuracy. You can also download the Vedantu app from Google play store to access these important questions along with the readymade so.
5. Is it enough to practice using Vedantu’s important Questions for Chapter 7 of Class 10 Maths?
Chapter 7 of Class 10 Maths requires extensive practice. The most significant course material in this regard is your NCERT textbook and its Solutions. After that, you can practice using Vedantu's Important Question for Chapter 7 of Class 10 Maths. These questions provide you with a ton of practice and are crucial for your board examinations. Another important thing is to practice using sample papers and previous years’ questions. All these together form the most crucial sources of your CBSE exam preparation.
6. Is Class 10 Mathematics Chapter 7 Coordinate Geometry easy?
Coordinate geometry is an important chapter for CBSE board examinations. It is a pretty straightforward chapter in which you can score perfect marks if you understand the concepts well. Questions of a total of 6 marks may be asked from this chapter.
Coordinate Geometry does require lots of practice and Vedantu's Important Questions for Chapter 7 of Class 10 Maths is the ideal place for this. Get tons of practice on a variety of questions thanks to Vedantu .
7. How many questions can I find on Vedantu’s Important Questions for Chapter 7 of Class 10 Maths?
Vedantu's Important Questions for Chapter 7 ‘Coordinate Geometry’ of Class 10 Maths contains 94 questions ranging from 1 to 4 marks along with many value-based questions.
Practising these many questions is bound to perfect your understanding of the chapter and in turn, provide much-needed practise for the CBSE Board examinations. As soon as you finish your NCERT textbook questions you must practice these questions regularly. Frequent practice at regular intervals will help you master all the Class 10 Mathematics chapters.
8. What are some important questions from Coordinate Geometry?
Few Important Questions from Chapter 7 ‘Coordinate Geometry’ of Class 10 Maths are as follows:
If, Q (0,1) is equidistant from P (5, -3) and R (x, 6), find the values of x. also, find the distances QR and PR. (4 Marks)
Find the centre of a circle passing through the points (6, -6), (3, -7), and (3, 3). (3 Marks)
Find the relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5)
9. What are the important topics of Chapter 7 ‘Coordinate Geometry’ of Class 10 Maths ?
Important topics covered in Coordinate Geometry are as follows:
a. Distance Formula
b. Section Formula
c. Special Case of the midpoint of a line segment joining two points
d. Area of a Triangle
To practice important questions from this chapter, visit Vedantu's Important Questions for Chapter 7 ‘Coordinate Geometry’ of Class 10 Maths . These are handpicked from the NCERT textbook, sample papers, and previous years’ question papers. Hence these are the apt test practice tool for Class 10 Mathematics CBSE Board exams. The study material provided by Vedantu is available to download from its website (vedantu.com) absolutely free of cost.
CBSE Class 10 Maths Important Questions
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Case Study Class 10 Maths Questions
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Download the app to get CBSE Sample Papers 2023-24, NCERT Solutions (Revised), Most Important Questions, Previous Year Question Bank, Mock Tests, and Detailed Notes.
Now, CBSE will ask only subjective questions in class 10 Maths case studies. But if you search over the internet or even check many books, you will get only MCQs in the class 10 Maths case study in the session 2022-23. It is not the correct pattern. Just beware of such misleading websites and books.
We advise you to visit CBSE official website ( cbseacademic.nic.in ) and go through class 10 model question papers . You will find that CBSE is asking only subjective questions under case study in class 10 Maths. We at myCBSEguide helping CBSE students for the past 15 years and are committed to providing the most authentic study material to our students.
Here, myCBSEguide is the only application that has the most relevant and updated study material for CBSE students as per the official curriculum document 2022 – 2023. You can download updated sample papers for class 10 maths .
First of all, we would like to clarify that class 10 maths case study questions are subjective and CBSE will not ask multiple-choice questions in case studies. So, you must download the myCBSEguide app to get updated model question papers having new pattern subjective case study questions for class 10 the mathematics year 2022-23.
Class 10 Maths has the following chapters.
- Real Numbers Case Study Question
- Polynomials Case Study Question
- Pair of Linear Equations in Two Variables Case Study Question
- Quadratic Equations Case Study Question
- Arithmetic Progressions Case Study Question
- Triangles Case Study Question
- Coordinate Geometry Case Study Question
- Introduction to Trigonometry Case Study Question
- Some Applications of Trigonometry Case Study Question
- Circles Case Study Question
- Area Related to Circles Case Study Question
- Surface Areas and Volumes Case Study Question
- Statistics Case Study Question
- Probability Case Study Question
Format of Maths Case-Based Questions
CBSE Class 10 Maths Case Study Questions will have one passage and four questions. As you know, CBSE has introduced Case Study Questions in class 10 and class 12 this year, the annual examination will have case-based questions in almost all major subjects. This article will help you to find sample questions based on case studies and model question papers for CBSE class 10 Board Exams.
Maths Case Study Question Paper 2023
Here is the marks distribution of the CBSE class 10 maths board exam question paper. CBSE may ask case study questions from any of the following chapters. However, Mensuration, statistics, probability and Algebra are some important chapters in this regard.
| I | NUMBER SYSTEMS | 06 |
| II | ALGEBRA | 20 |
| III | COORDINATE GEOMETRY | 06 |
| IV | GEOMETRY | 15 |
| V | TRIGONOMETRY | 12 |
| V | MENSURATION | 10 |
| VI | STATISTICS & PROBABILITY | 11 |
Case Study Question in Mathematics
Here are some examples of case study-based questions for class 10 Mathematics. To get more questions and model question papers for the 2021 examination, download myCBSEguide Mobile App .
Case Study Question – 1
In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021–22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year.
- Find the production in the 1 st year.
- Find the production in the 12 th year.
- Find the total production in first 10 years. OR In which year the total production will reach to 15000 cars?
Case Study Question – 2
In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.
- Find the distance between Lucknow (L) to Bhuj(B).
- If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
- Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P) OR Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).
Case Study Question – 3
- Find the distance PA.
- Find the distance PB
- Find the width AB of the river. OR Find the height BQ if the angle of the elevation from P to Q be 30 o .
Case Study Question – 4
- What is the length of the line segment joining points B and F?
- The centre ‘Z’ of the figure will be the point of intersection of the diagonals of quadrilateral WXOP. Then what are the coordinates of Z?
- What are the coordinates of the point on y axis equidistant from A and G? OR What is the area of area of Trapezium AFGH?
Case Study Question – 5
The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.
- If the first circular row has 30 seats, how many seats will be there in the 10th row?
- For 1500 seats in the auditorium, how many rows need to be there? OR If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after 10 th row?
- If there were 17 rows in the auditorium, how many seats will be there in the middle row?
Case Study Question – 6
- Draw a neat labelled figure to show the above situation diagrammatically.
- What is the speed of the plane in km/hr.
More Case Study Questions
We have class 10 maths case study questions in every chapter. You can download them as PDFs from the myCBSEguide App or from our free student dashboard .
As you know CBSE has reduced the syllabus this year, you should be careful while downloading these case study questions from the internet. You may get outdated or irrelevant questions there. It will not only be a waste of time but also lead to confusion.
Here, myCBSEguide is the most authentic learning app for CBSE students that is providing you up to date study material. You can download the myCBSEguide app and get access to 100+ case study questions for class 10 Maths.
How to Solve Case-Based Questions?
Questions based on a given case study are normally taken from real-life situations. These are certainly related to the concepts provided in the textbook but the plot of the question is always based on a day-to-day life problem. There will be all subjective-type questions in the case study. You should answer the case-based questions to the point.
What are Class 10 competency-based questions?
Competency-based questions are questions that are based on real-life situations. Case study questions are a type of competency-based questions. There may be multiple ways to assess the competencies. The case study is assumed to be one of the best methods to evaluate competencies. In class 10 maths, you will find 1-2 case study questions. We advise you to read the passage carefully before answering the questions.
Case Study Questions in Maths Question Paper
CBSE has released new model question papers for annual examinations. myCBSEguide App has also created many model papers based on the new format (reduced syllabus) for the current session and uploaded them to myCBSEguide App. We advise all the students to download the myCBSEguide app and practice case study questions for class 10 maths as much as possible.
Case Studies on CBSE’s Official Website
CBSE has uploaded many case study questions on class 10 maths. You can download them from CBSE Official Website for free. Here you will find around 40-50 case study questions in PDF format for CBSE 10th class.
10 Maths Case Studies in myCBSEguide App
You can also download chapter-wise case study questions for class 10 maths from the myCBSEguide app. These class 10 case-based questions are prepared by our team of expert teachers. We have kept the new reduced syllabus in mind while creating these case-based questions. So, you will get the updated questions only.
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Get NCERT Solutions of all Exercise Questions and Examples of Chapter 7 Class 10 Coordinate Geometry. All questions have been solved in an easy to understand way with detailed explanation of each and every step.
Answers to optional exercise is also given
In Coordinate Geometry of Class 9, we learned what is x and y coordinate of a point.
In this chapter, we will learn
- Coordinates of points in x-axis (x, 0) and y-axis (0, y)
- How to find distance between two points using Distance Formula
- Checking if points form a triangle, or an isoceles triangle, or a square, rectangle. (To do this, we need to learn properties of parallelogram )
- Checking if 3 points are collinear using Distance Formula
- Finding points equidistant to given points
- Then, we will learn about Section Formula - Finding coordinates of a point that divides line joining two points in some ratio
- Finding coordinates of mid-point of a line using Section Formula
- Finding ratio when coordinates of point of intersection is given
- Using properties of parallelogram to do some questions on Section Formula (like finding coordinates of a point, when 4 vertices of parallelogram are given)
- Finding Area of triangle when coordinates of all 3 vertices are given
- Proving 3 points collinear using Area of Triangle Formula
- Finding Area of Quadrialteral using Area of Triangle Formula (dividing Quadrilateral into 2 triangles and finding area)
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Are you looking for a reliable source to download Class 10 Maths case study questions in PDF format? Look no further! In this article, we will provide you with a comprehensive collection of case study questions specifically designed for Class 10 Maths Case Study Questions . Whether you are a student or a teacher, these case study questions will prove to be a valuable resource in your preparation or teaching process.
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If you want to want to prepare all the tough, tricky & difficult questions for your upcoming exams, this is where you should hang out. CBSE Case Study Questions for Class 10 will provide you with detailed, latest, comprehensive & confidence-inspiring solutions to the maximum number of Case Study Questions covering all the topics from your NCERT Text Books !
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CBSE 10th Maths: Case Study Questions With Answers
Students taking the 10th board examinations will see new kinds of case study questions in class. The board initially incorporated case study questions into the board exam. The chapter-by-chapter case study question and answers are available here.
Chapterwise Case Study Questions for Class 10 Mathematics
Case study questions are an essential component of the Class 10 Mathematics curriculum. They provide students with real-world scenarios where they can apply mathematical concepts and problem-solving skills. By analyzing and solving these case study questions, students develop a deeper understanding of the subject and improve their critical thinking abilities.
The above Case studies for Class 10 Maths will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 10 Mathematics Case Studies have been developed by experienced teachers of schools.studyrate.in for the benefit of Class 10 students.
- Class 10th Science Case Study Questions
Benefits of Case Study Questions for Class 10 Mathematics
Case study questions offer several benefits to both students and teachers. Here are some key advantages:
- Practical Application : Case study questions bridge the gap between theory and real-life situations, allowing students to apply mathematical concepts in practical scenarios.
- Analytical Thinking : By solving case study questions, students enhance their analytical thinking and problem-solving skills.
- Conceptual Clarity : Case study questions help reinforce the fundamental concepts of mathematics, leading to improved conceptual clarity.
- Exam Preparation : Practicing case study questions prepares students for their Class 10 Mathematics exams, as they become familiar with the question formats and types.
- Comprehensive Assessment : Teachers can use case study questions to assess students’ understanding of various mathematical concepts in a comprehensive manner.
How to Use Case Study Questions Effectively
To make the most out of the case study questions, follow these effective strategies:
- Read the question carefully : Understand the given scenario and identify the mathematical concepts involved.
- Analyze the problem : Break down the problem into smaller parts and determine the approach to solve it.
- Apply relevant formulas and concepts : Utilize your knowledge of the subject to solve the case study question.
- Show your working : Clearly demonstrate the steps and calculations involved in reaching the solution.
- Check your answer : Always verify if your solution aligns with the given problem and recheck calculations for accuracy.
Tips for Solving Case Study Questions
Here are some useful tips to excel in solving case study questions:
- Practice regularly : Regular practice will enhance your problem-solving skills and familiarity with different question formats.
- Understand the concepts: Ensure you have a strong foundation in the underlying mathematical concepts related to each chapter.
- Work on time management : Practice solving case study questions within a stipulated time to improve your speed and efficiency during exams.
- Seek clarification : If you encounter any doubts or difficulties, don’t hesitate to seek guidance from your teacher or peers.
Case study questions are an invaluable resource for Class 10 Mathematics students. They provide practical application opportunities and strengthen conceptual understanding. By utilizing the chapter-wise case study questions provided in this article, students can enhance their problem-solving skills, prepare effectively for exams, and develop a deeper appreciation for the subject.
FAQs on Class 10 Maths Case Study Questions
Q1: can i download the class 10 maths case study questions in pdf format.
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Yes, the case study questions presented in this article are designed to align with the latest Class 10 Mathematics curriculum.
Q3: How can case study questions improve my exam preparation?
Case study questions help you understand the practical application of mathematical concepts, enabling you to approach exam questions with greater confidence and clarity.
Q5: Where can I find more resources for Class 10 Mathematics preparation?
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- Math Article
- Coordinate Geometry For Class 10
Coordinate Geometry Class 10 Notes
Cbse class 10 maths coordinate geometry notes:- download pdf here, class 10 maths chapter 7 coordinate geometry notes.
The complete notes on coordinate geometry for Class 10 are provided here. Coordinate geometry teaches us the location of a point on a plane. For example, the coordinates of a point are (x, y), where x-coordinate (abscissa) denotes the distance of a point from the y-axis and y-coordinate (ordinate) denotes the distance of the point from the x-axis. Now we will learn to find the distance between two points and the area of a triangle using the distance formula when the coordinates of the points are given. Go through the below article and learn the points on the coordinate plane, distance formulas, section formulas and so on with a detailed explanation.
Students can refer to the short notes and MCQ questions along with a separate solution pdf of this chapter for quick revision from the links below:
- Coordinate Geometry Short Notes
- Coordinate Geometry MCQ Practice Questions
- Coordinate Geometry MCQ Practice Solutions
Basics of Coordinate Geometry
For more information on the basics of coordinate geometry, watch the below video.
To know more about Coordinate Geometry, visit here .
Points on a Cartesian Plane
A pair of numbers locate points on a plane called the coordinates . The distance of a point from the y-axis is known as abscissa or x-coordinate. The distance of a point from the x-axis is called ordinate or y-coordinate.
Example: Consider a point P(3, 2), where 3 is the abscissa, and 2 is the ordinate. 3 represents the distance of point P from the y-axis, and 2 represents the distance of point P from the x-axis.
Distance Formula
Distance between two points on the same coordinate axes.
The distance between two points that are on the same axis (x-axis or y-axis) is given by the difference between their ordinates if they are on the y-axis, else by the difference between their abscissa if they are on the x-axis.
Distance AB = 6 – (-2) = 8 units
Distance CD = 4 – (-8) = 12 units
Distance between Two Points Using Pythagoras Theorem
Let P(x 1 , y 1 ) and Q(x 2 , y 2 ) be any two points on the cartesian plane.
Draw lines parallel to the axes through P and Q to meet at T.
ΔPTQ is right-angled at T.
By Pythagoras Theorem ,
PQ 2 = PT 2 + QT 2
= (x 2 – x 1 ) 2 + (y 2 – y 1 ) 2
Distance between any two points (x 1 , y 1 ) and (x 2 , y 2 ) is given by
Where d is the distance between the points (x 1 ,y 1 ) and (x 2 ,y 2 ).
To know more about Distance Formula, visit here .
Section Formula
If the point P(x, y) divides the line segment joining A(x 1 , y 1 ) and B(x 2 , y 2 ) internally in the ratio m:n , then, the coordinates of P are given by the section formula as:
For more information on Section Formula, watch the below video
To know more about Section Formula, visit here .
Finding Ratio given the points
To find the ratio in which a given point P(x, y) divides the line segment joining A(x 1 , y 1 ) and B(x 2 , y 2 ),
- Assume that the ratio is k : 1
- Substitute the ratio in the section formula for any of the coordinates to get the value of k.
When x1, x2 and x are known, k can be calculated. The same can be calculated from the y- coordinate also.
Example: Find the ratio when point (– 4, 6) divide the line segment joining the points A(– 6, 10) and B(3, – 8)?
Solution: Let the ratio be m:n.
We can write the ratio as:
m/n : 1 or k:1
Suppose (-4, 6) divide the line segment AB in k:1 ratio.
Now using the section formula, we have the following;
-4 = (3k-6)/(k+1)
– 4k – 4 = 3k – 6
k : 1 = 2 : 7
Thus, the required ratio is 2:7.
The midpoint of any line segment divides it in the ratio 1 : 1 .
The coordinates of the midpoint(P) of line segment joining A(x 1 , y 1 ) and B(x 2 , y 2 ) is given by
Example: What is the midpoint of line segment PQ whose coordinates are P (-3, 3) and Q (1, 4), respectively.
Solution: Given, P (-3, 3) and Q (1, 4) are the points of line segment PQ.
Using midpoint formula, we have;
= (-2/2, 1/2)
= (-1, 1/2)
Points of Trisection
To find the points of trisection P and Q, which divides the line segment joining A(x 1 , y 1 ) and B(x 2 , y 2 ) into three equal parts:
i) AP : PB = 1 : 2
ii) AQ : QB = 2 : 1
Example: Find the coordinates of the points of trisection of the line segment joining the points A(2, – 2) and B(– 7, 4).
Solution: Let P and Q divide the line segment AB into three parts.
So, P and Q are the points of trisection here.
Let P divides AB in 1:2, thus by section formula, the coordinates of P are (1, 0)
Let Q divides AB in 2:1 ratio, then by section formula, the coordinates are (-4,2)
Thus, the point of trisection for line segment AB are (1,0) and (-4,2).
Centroid of a Triangle
If A(x 1 , y 1 ), B(x 2 , y 2 ), and C(x 3 , y 3 ) are the vertices of a ΔABC, then the coordinates of its centroid(P) are given by
Example: Find the coordinates of the centroid of a triangle whose vertices are given as (-1, -3), (2, 1) and (8, -4)
Solution: Given,
The coordinates of the vertices of a triangle are (-1, -3), (2, 1) and (8, -4)
The Centroid of a triangle is given by:
G = ((x 1 +x 2 +x 3 )/3 , (y 1 +y 2 +y 3 )/3 )
G = ((-1+2+8)/3 , (-3+1-4)/3)
G =( 9/3 , -6/3)
G = (3, -2)
Therefore, the centroid of a triangle, G = (3, -2)
Learn more: Centroid of a Triangle
Area from Coordinates
Area of a triangle given its vertices.
If A(x 1 , y 1 ),B(x 2 , y 2 ) and C(x 3 , y 3 ) are the vertices of a Δ ABC, then its area is given by
Where A is the area of the Δ ABC.
Example: Find the area of the triangle ABC whose vertices are A(1, 2), B(4, 2) and C(3, 5).
Using the formula given above,
Area = 9/2 square units.
Therefore, the area of a triangle ABC is 9/2 square units.
To know more about the Area of a Triangle, visit here .
Collinearity Condition
If three points A, B and C are collinear and B lies between A and C, then,
- AB + BC = AC. AB, BC, and AC can be calculated using the distance formula.
- The ratio in which B divides AC, calculated using the section formula for both the x and y coordinates separately, will be equal.
- The area of a triangle formed by three collinear points is zero.
Video Lesson on Coordinate Geometry Toughest Problems
Coordinate Geometry for Class 10 Problems
Determine the distance between the pair of points (a, b) and (-a, -b)
Let the given points be A(a, b) and B(-a, -b)
We know that the distance formula is:
AB = √[(x 2 -x 1 ) 2 +(y 2 -y 1 ) 2 ]
(x 1 , y 1 ) = (a, b)
(x 2 , y 2 ) = (-a, -b)
Now, substitute the values in the distance formula, we get
AB = √[(-a-a) 2 +(-b-b) 2 ]
AB = √[(-2a) 2 + (-2b) 2 ]
AB = √[4a 2 +4b 2 ]
AB = √[4(a 2 +b 2 )]
AB = √4. √[a 2 +b 2 ]
AB = 2.√[a 2 +b 2 ].
Hence, the distance between two points (a, b) and (-a, -b) is 2√[a 2 +b 2 ].
Determine the ratio in which the line segment joining the points A(1, -5) and B(-4, 5) is divided by the x-axis. Also, find the coordinates of the point of division.
Given that, the point P is on the x-axis. Hence, the y-coordinate is 0. Hence, the point is of the form P(x, 0).
Now, we have to find the ratio. Let the ratio be k:1.
Given Points: A(1, -5) and B = (-4, 5).
(x 1 , y 1 ) = (1, -5)
(x 2 , y 2 ) = (-4, 5)
m 1 = k, m 2 = 1
We know that the section formula is:
y= [m 1 y 2 +m 2 y 1 ]/[m 1 +m 2 ]
Now, substitute the values in the section formula, we get
y = [k(5) + 1(-5)]/[k+1]
y = [5k-5]/[k+1]
(5k-5)/(k+1) = 0
Hence, the ratio k:1 = 1:1
Finding x-coordinate:
x= [m 1 x 2 +m 2 x 1 ]/[m 1 +m 2 ]
x = [k(-4) + 1(1)]/(k+1)
Now, substitute k=1 in the above equation, we get
x = [1(-4) + 1(1)]/(1+1)
x = (-4+1)/2
Hence, the coordinate of the point is P(x, 0) = P(-3/2, 0).
Related Articles
- NCERT Solutions for Class 10 Chapter 7 Coordinate Geometry
- Class 10 Maths Chapter 7 Coordinate Geometry MCQs
- Important Questions Class 10 Maths Chapter 7 Coordinate Geometry
- Two Dimensional Coordinate Geometry
- Coordinate Geometry Formulas
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Case Study Class 10 Maths Questions and Answers (Download PDF)
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Case Study Class 10 Maths
If you are looking for the CBSE Case Study class 10 Maths in PDF, then you are in the right place. CBSE 10th Class Case Study for the Maths Subject is available here on this website. These Case studies can help the students to solve the different types of questions that are based on the case study or passage.
CBSE Board will be asking case study questions based on Maths subjects in the upcoming board exams. Thus, it becomes an essential resource to study.
The Case Study Class 10 Maths Questions cover a wide range of chapters from the subject. Students willing to score good marks in their board exams can use it to practice questions during the exam preparation. The questions are highly interactive and it allows students to use their thoughts and skills to solve the given Case study questions.
Download Class 10 Maths Case Study Questions and Answers PDF (Passage Based)
Download links of class 10 Maths Case Study questions and answers pdf is given on this website. Students can download them for free of cost because it is going to help them to practice a variety of questions from the exam perspective.
Case Study questions class 10 Maths include all chapters wise questions. A few passages are given in the case study PDF of Maths. Students can download them to read and solve the relevant questions that are given in the passage.
Students are advised to access Case Study questions class 10 Maths CBSE chapter wise PDF and learn how to easily solve questions. For gaining the basic knowledge students can refer to the NCERT Class 10th Textbooks. After gaining the basic information students can easily solve the Case Study class 10 Maths questions.
Case Study Questions Class 10 Maths Chapter 1 Real Numbers
Case Study Questions Class 10 Maths Chapter 2 Polynomials
Case Study Questions Class 10 Maths Chapter 3 Pair of Equations in Two Variables
Case Study Questions Class 10 Maths Chapter 4 Quadratic Equations
Case Study Questions Class 10 Maths Chapter 5 Arithmetic Progressions
Case Study Questions Class 10 Maths Chapter 6 Triangles
Case Study Questions Class 10 Maths Chapter 7 Coordinate Geometry
Case Study Questions Class 10 Maths Chapter 8. Introduction to Trigonometry
Case Study Questions Class 10 Maths Chapter 9 Some Applications of Trigonometry
Case Study Questions Class 10 Maths Chapter 10 Circles
Case Study Questions Class 10 Maths Chapter 12 Areas Related to Circles
Case Study Questions Class 10 Maths Chapter 13 Surface Areas & Volumes
Case Study Questions Class 10 Maths Chapter 14 Statistics
Case Study Questions Class 10 Maths Chapter 15 Probability
How to Solve Case Study Based Questions Class 10 Maths?
In order to solve the Case Study Based Questions Class 10 Maths students are needed to observe or analyse the given information or data. Students willing to solve Case Study Based Questions are required to read the passage carefully and then solve them.
While solving the class 10 Maths Case Study questions, the ideal way is to highlight the key information or given data. Because, later it will ease them to write the final answers.
Case Study class 10 Maths consists of 4 to 5 questions that should be answered in MCQ manner. While answering the MCQs of Case Study, students are required to read the paragraph as they can get some clue in between related to the topics discussed.
Also, before solving the Case study type questions it is ideal to use the CBSE Syllabus to brush up the previous learnings.
Features Of Class 10 Maths Case Study Questions And Answers Pdf
Students referring to the Class 10 Maths Case Study Questions And Answers Pdf from Selfstudys will find these features:-
- Accurate answers of all the Case-based questions given in the PDF.
- Case Study class 10 Maths solutions are prepared by subject experts referring to the CBSE Syllabus of class 10.
- Free to download in Portable Document Format (PDF) so that students can study without having access to the internet.
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- Case study class 10 maths helps in exam preparation since, CBSE Class 10 Question Papers contain case-based questions.
- It allows students to utilise their learning to solve real life problems.
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QB365 Provides the updated CASE Study Questions for Class 10 Maths, and also provide the detail solution for each and every case study questions . Case study questions are latest updated question pattern from NCERT, QB365 will helps to get more marks in Exams
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Check Case Study Questions for Class 10 Maths Chapter 7 - Coordinate Geometry. CASE STUDY 1: In order to conduct Sports Day activities in your School, lines have been drawn with chalk powder at a ...
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Case Study Questions for Class 10 Maths Chapter 7 Coordinate Geometry Last modified on: 1 year ago Reading Time: 3 Minutes
Information about Case Based Questions: Coordinate Geometry covers topics like Study Case - 1, Case Study - 2, Study Case - 3 and Case Based Questions: Coordinate Geometry Example, for Class 10 2024 Exam.
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Case Study Class 10 Maths Questions First of all, we would like to clarify that class 10 maths case study questions are subjective and CBSE will not ask multiple-choice questions in case studies. So, you must download the myCBSEguide app to get updated model question papers having new pattern subjective case study questions for class 10 the mathematics year 2022-23.
CBSE Class 10 Maths Case Study : We have provided the PDF File of CBSE Class 10 Maths case study based Questions, MCQs, Assertion with Resion and solutions.
It helps us to study geometry using algebra, and understand algebra with the help of geometry. Because of this, coordinate geometry is widely applied in various fields such as physics, engineering, navigation, seismology and art!
RD Sharma Solutions Class 10 Maths Chapter 14 - Free PDF Download The RD Sharma Solutions for Class 10 Maths Chapter 14 - Co-ordinate Geometry explain each concept in a comprehensive manner to help students obtain a thorough knowledge of concepts. Coordinates are ordered pairs of numbers, and the study of Geometry using coordinates is called Co-ordinate Geometry. Class 10 Mathematics ...
Get NCERT Solutions of all Exercise Questions and Examples of Chapter 7 Class 10 Coordinate Geometry. All questions have been solved in an easy to understand way with detailed explanation of each and every step. Answers to optional exercise is also given. In Coordinate Geometry of Class 9, we learned what is x and y coordinate of a point.
Case Study Questions Class 10 Maths PDF In class 10 Board Exam 2021, You will find a new type of case-based questions. This is for the first time when you are going to face these type of questions in the board examination. CBSE has introduced these types of questions to better understand each chapter of class 10 maths. We have analysed CBSE Sample Paper 2021 and we found many changes in the ...
In this article, we will provide you with a comprehensive collection of case study questions specifically designed for Class 10 Maths Case Study Questions. Whether you are a student or a teacher, these case study questions will prove to be a valuable resource in your preparation or teaching process. Download Books for Boards.
NCERT Solutions for Class 10 Maths Chapter 7 - CBSE Free PDF Download. NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry covers all the exercises provided in the NCERT textbook. These NCERT solutions, prepared by experts at BYJU'S, are comprehensive study material for the students preparing for the CBSE Class 10 board ...
Important Questions & Answers For Class 10 Maths Chapter 7 Coordinate Geometry Q. 1: Find the distance of the point P (2, 3) from the x-axis.
Download case study question pdfs for CBSE Class 10th Maths, CBSE Class 10th English, CBSE Class 10th Sciece, CBSE Class 10th SST. As the CBSE 10th Term-1 Board Exams are approaching fast, you can use these worksheets for FREE for practice by students for the new case study formats for CBSE introduced this year.
The complete notes on coordinate geometry for Class 10 are provided here. Coordinate geometry teaches us the location of a point on a plane. For example, the coordinates of a point are (x, y), where x-coordinate (abscissa) denotes the distance of a point from the y-axis and y-coordinate (ordinate) denotes the distance of the point from the x ...
Case Study Class 10 Maths: Here, you will get class 10 maths case study questions and answers pdf at free of cost. Along with you can also download case study questions class 10 maths chapter wise for getting higher marks in board examinations.