CBSE Class 10 Coordinate geometry Sure Shot Questions Set A

Mathematics
Download PDF

Read and download the CBSE Class 10 Coordinate geometry Sure Shot Questions Set A. Designed for 2025-26, this advanced study material provides Class 10 Mathematics students with detailed revision notes, sure-shot questions, and detailed answers. Prepared by expert teachers and they follow the latest CBSE, NCERT, and KVS guidelines to ensure you get best scores.

Advanced Study Material for Class 10 Mathematics Chapter 7 Coordinate Geometry

To achieve a high score in Mathematics, students must go beyond standard textbooks. This Class 10 Chapter 7 Coordinate Geometry study material includes conceptual summaries and solved practice questions to improve you understanding.

Class 10 Mathematics Chapter 7 Coordinate Geometry Notes and Questions

 

CBSE Class 10 Coordinate geometry Sure Shot Questions Set A. There are many more useful educational material which the students can download in pdf format and use them for studies. Study material like concept maps, important and sure shot question banks, quick to learn flash cards, flow charts, mind maps, teacher notes, important formulas, past examinations question bank, important concepts taught by teachers. Students can download these useful educational material free and use them to get better marks in examinations.  Also refer to other worksheets for the same chapter and other subjects too. Use them for better understanding of the subjects.

1. Find the distance between the following points:

(i) A(9, 3) and (15, 11)            (ii) A(7, – 4) and b(–5, 1).

(iii) A(–6, –4) and B(9, –12)     (iv) A(1, –3) and B(4, –6)

(v) P(a + b, a – b) and Q(a – b, a + b)

(vi) P(a sin a, a cos a) and Q(a cos a, –a sin a)

2. If A(6, –1), B(1, 3) and C(k, 8) are three points such that AB= BC, find the value of k.

3. Find all the possible value of a for which the distance between the points A(a, –1) and B(5, 3) is 5 units.

4. Determine, whether each of the given points (–2, 1), (2, –2) and (5, 2) are the vertices of right angle.

5. Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear.

6. By distance formula, show that the points (1, –1), (5, 2) and (9, 5) are collinear.

7. Find the value of k if the points A(2, 3), B(4, k) and C(6, –3) are collinear.

8. Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear.

9. Find the point on x-axis which is equidistant from (–2, 5) and (2, –3).

10. Find the point on x-axis which is equidistant from (7, 6) and (–3, 4).

11. Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).

12. Find a point on the y-axis which is equidistant from the points A(6, 5) and B(– 4, 3).

13. Find a point on the y-axis which is equidistant from the points A(5, 2) and B(– 4, 3).

14. Find a point on the y-axis which is equidistant from the points A(5, – 2) and B(– 3, 2).

15. Find the point on y-axis, each of which is at a distance of 13 units from the point (–5, 7).

16. Find the point on x-axis, each of which is at a distance of 10 units from the point (11, –8).

17. Find the values of k for which the distance between the points A(k, –5) and B(2, 7) is 13 units.

18. Prove that the points A(–3, 0), B(1, –3) and C(4, 1) are the vertices of an isosceles right-angled triangle. Find the area of this triangle.

19. Prove that the points A(a, a), B(–a, –a) and C(– 3 a, 3 a) are the vertices of an equilateral triangle. Calculate the area of this triangle.

20. If the distance of P(x, y) from A(5, 1) and B(–1, 5) are equal. Prove that 3x = 2y.
 
21. Show that the points A(1, 2), B(5, 4), C(3, 8) and D(–1, 6) are vertices of a square.
 
22. Show that the points A(5, 6), B(1, 5), C(2, 1) and D(6, 2) are vertices of a square.
 
23. Show that the points A(0, –2), B(3, 1), C(0, 4) and D(–3, 1) are vertices of a square. Also find its area.
 
24. Show that the points A(6, 2), B(2, 1), C(1, 5) and D(5, 6) are vertices of a square. Also find its area.
 
25. Show that the points A(–4, –1), B(–2, –4), C(4, 0) and D(2, 3) are vertices of a rectangle. Also find its area.
 
26. Prove that the points A(2, –2), B(14, 10), C(11, 13) and D(–1, 1) are vertices of a rectangle. Find the area of this rectangle.
 
27. Show that the points A(1, –3), B(13, 9), C(10, 12) and D(–2, 0) are vertices of a rectangle.
 
28. Show that the points A(1, 0), B(5, 3), C(2, 7) and D(–2, 4) are vertices of a rhombus.
 
29. Prove that the points A(2, –1), B(3, 4), C(–2, 3) and D(–3, –2) are vertices of a rhombus. Find the area of this rhombus.
 
30. Show that the points A(–3, 2), B(–5, –5), C(2, –3) and D(4, 4) are vertices of a rhombus. Find the area of this rhombus.
 
31. Prove that the points A(–2, –1), B(1, 0), C(4, 3) and D(1, 2) are vertices of a parallelogram.
 
32. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (– 1, 4) and (– 2, – 1) taken in order.
 
33. Find the coordinates of the circumcentre of a triangle whose vertices are A(4, 6), B(0, 4) and C(6, 2). Also, find its circumradius.
 
34. Find the coordinates of the circumcentre of a triangle whose vertices are A(3, 0), B(–1, –6) and C(4, –1). Also, find its circumradius.
 
35. Find the coordinates of the circumcentre of a triangle whose vertices are A(8, 6), B(8, –2) and C(2, –2). Also, find its circumradius.
 
36. Find the coordinates of the centre of a circle passing through the points A(2, 1), B(5, –8) and C(2, –9). Also find the radius of this circle.
 
37. Find the coordinates of the centre of a circle passing through the points A(–2, –3), B(–1, 0) and C(7, –6). Also find the radius of this circle.
 
38. Find the coordinates of the centre of a circle passing through the points A(1, 2), B(3, –4) and C(5, –6). Also find the radius of this circle.
 
39. Find the coordinates of the centre of a circle passing through the points A(0, 0), B(–2, 1) and C(– 3, 2). Also find the radius of this circle.
 
40. Find the centre of a circle passing through the points (6, – 6), (3, – 7) and (3, 3).
 
41. Find the coordinates of the point equidistant from three given points A(5, 3), B(5, –5) and C(1, – 5).
 
42. If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken in order, find the value of p.
 
43. Find a relation between x and y such that the point (x , y) is equidistant from the points (7, 1) and (3, 5).
 
44. Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.
 
45. Find the values of y for which the distance between the points P(2, – 3) and Q(10, y) is 10 units.
 
46. 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.
 
47. If two vertices of an equilateral triangle be O(0, 0) and A(3, √3 ), find the coordinates of its third vertex.
 
48. The two opposite vertices of a square are (–1, 2) and (3, –2). Find the coordinates of the other two vertices.
 
49. The two opposite vertices of a square are (1, –6) and (5, 4). Find the coordinates of the other two vertices.
 
50. Prove that the points A(7, 10), B(–2, 5) and C(3, –4) are the vertices of an isosceles right triangle.
 
51. Show that the points A(–5, 6), B(3, 0) and C(9, 8) are the vertices of an isosceles right angled triangle. Find the area of this triangle.
 
52. Show that the points A(2, 1), B(5, 2), C(6, 4) and D(3, 3) are the angular points of parallelogram. Is this figure a rectangle?
 
53. Show that the points O(0, 0), A(3, √3 ) and B(3, – √3 ) are the vertices of an equilateral triangle. Find the area of this triangle.
 
54. Prove that the points A(3, 0), B(6, 4) and C(–1, 3) are the vertices of a right triangle. Also prove that these are vertices of an isosceles triangle.
 
55. If P and Q are two points whose coordinates are (at2, 2at) and (a/t2 , 2a/t) respectively and S is the point (a, 0). Show that 1/SP +1/ SQ  is independent of t.
 
56. If the points A(4, 3) and B(x, 5) are on the circle with centre O(2, 3), find the value of x.
 
57. Find the relation between x and y if point P(x, y) lies on the perpendicular bisector of the line joining the points (3, 6) and (–3, 4).
 
58. Find the relation between x and y if point P(x, y) lies on the perpendicular bisector of the line joining the points (7, 1) and (3, 5).
 
59. If A, B and P are the points (–4, 3), (0, –2) and (α, β) respectively and P is equidistant from A and B, show that 8α - 10β + 21 = 0.
 
60. If the points (5, 4) and (x, y) are equidistant from the point (4, 5), prove that x2 + y2 – 8x – 10y + 39 = 0.
 
61. Find the coordinates of the point whish is at a distance of 2 units from (5, 4) and 10 units from (11, –2).
 
62. If two vertices of an equilateral triangle are (0, 0) and (3, 0), find the third vertex.
 
63. The centre of a circle is (2α–1, 3α+1) and it passes through the point (–3, –1). If a diameter of the circle is of length 20 units, find the value of α.
 
64. If the point P(x, y) is equidistant from the points A(5, 1) and B(–1, 5), prove that x = y.
 
65. Find the value of k if the point P(0, 2) is equidistant from (3, k) and (k, 5).
 
66. Let the opposite angular points of a square be (3, 4) and (1, –1). Find the coordinates of the remaining angular points.
 
67. Prove that the points (2x, 4a), (2a, 6a) and (2a + 3 a, 5a) are the vertices of an equilateral triangle.
 
68. An equilateral triangle has two vertices at the points (3, 4) and (–2, 3), find the coordinates of the third vertex.
 
69. Two vertex of an isosceles triangle are (2, 0) and (2, 5). Find the third vertex if the length of the equal sides is 3.
 
70. The coordinates of the point P are (–3, 2). Find the coordinates of the point Q which lies on the line joining P and origin such that OP = OQ.

Please click the link below to download CBSE Class 10 Coordinate geometry Sure Shot Questions Set A.

Chapter 01 Real Numbers
CBSE Class 10 Real Numbers Important Formulas and concepts for exams
CBSE Class 10 Real Numbers Sure Shot Questions
Chapter 02 Polynomials
CBSE Class 10 Polynomials Important Formulas and concepts for exams
CBSE Class 10 Polynomials Sure Shot Questions
Chapter 03 Pair of Linear Equations in Two Variables
CBSE Class 10 Pair of linear equations Important Formulas and concepts for exams
CBSE Class 10 Pair of Linear Equations in Two Variables Sure Shot Questions Set A
CBSE Class 10 Pair of Linear Equations in Two Variables Sure Shot Questions Set B
CBSE Class 10 Pair of Linear Equations in Two Variables Sure Shot Questions Set C
CBSE Class 10 Pair of Linear Equations in Two Variables Sure Shot Questions Set D
Chapter 04 Quadratic Equations
CBSE Class 10 Quadratic Equations Important Formulas and concepts for exams
CBSE Class 10 Quadratic Equations Sure Shot Questions Set A
CBSE Class 10 Quadratic Equations Sure Shot Questions Set B
CBSE Class 10 Quadratic Equations Sure Shot Questions Set C
CBSE Class 10 Quadratic Equations Sure Shot Questions Set D
CBSE Class 10 Quadratic Equations Sure Shot Questions Set E
Chapter 05 Arithmetic Progression
CBSE Class 10 Arithmetic Progression Important Formulas and concepts for exams
CBSE Class 10 Arithmetic Progressions Sure Shot Questions Set A
CBSE Class 10 Arithmetic Progressions Sure Shot Questions Set B
Chapter 06 Triangles
CBSE Class 10 Triangles Important Formulas and concepts for exams
CBSE Class 10 Triangles Sure Shot Questions
Chapter 07 Coordinate Geometry
CBSE Class 10 Coordinate Geometry Important Formulas and concepts for exams
CBSE Class 10 Coordinate geometry Sure Shot Questions Set A
CBSE Class 10 Coordinate geometry Sure Shot Questions Set B
CBSE Class 10 Coordinate geometry Sure Shot Questions Set C
CBSE Class 10 Coordinate geometry Sure Shot Questions Set D
Chapter 08 Introduction to Trigonometry
CBSE Class 10 Application of Trigonometry Important Formulas and concepts for exams
CBSE Class 10 Application of Trigonometry Sure Shot Questions Set A
CBSE Class 10 Introduction to Trigonometry Important Formulas and concepts for exams
CBSE Class 10 Introduction to Trigonometry Sure Shot Questions Set A
CBSE Class 10 Introduction to Trigonometry Sure Shot Questions Set B
CBSE Class 10 Introduction to Trigonometry Sure Shot Questions Set C
CBSE Class 10 Introduction to Trigonometry Sure Shot Questions Set D
CBSE Class 10 Introduction to Trigonometry Sure Shot Questions Set E
CBSE Class 10 Introduction to Trigonometry Sure Shot Questions Set F
Chapter 10 Circles
CBSE Class 10 Circles Important Formulas and concepts for exams
CBSE Class 10 Circles Sure Shot Questions
Chapter 11 Areas related to Circles
CBSE Class 10 Areas related to Circles Sure Shot Questions Set A
Chapter 12 Surface Area and Volume
CBSE Class 10 Surface Areas and Volumes Important Formulas and concepts for exams
CBSE Class 10 Surface Areas and Volumes Sure Shot Questions Set A
CBSE Class 10 Surface Areas and Volumes Sure Shot Questions Set B
Chapter 13 Statistics
CBSE Class 10 Statistics Important Formulas and concepts for exams
CBSE Class 10 Statistics Sure Shot Questions Set A
CBSE Class 10 Statistics Sure Shot Questions Set B
CBSE Class 10 Statistics Sure Shot Questions Set C
CBSE Class 10 Statistics Sure Shot Questions Set E
Chapter 14 Probability
CBSE Class 10 Probability Important Formulas and concepts for exams
CBSE Class 10 Probability Sure Shot Questions Set A
CBSE Class 10 Probability Sure Shot Questions Set B
CBSE Class 10 Probability Sure Shot Questions Set C
CBSE Class 10 Probability Sure Shot Questions Set D
CBSE Class 10 Probability Sure Shot Questions Set E
CBSE Class 10 Probability Sure Shot Questions Set F
CBSE Class 10 Probability Sure Shot Questions Set G
z Case Study Class 10 Mathematics
CBSE Class 10 Areas related to circles Important Formulas and concepts for exams
CBSE Class 10 Areas related to circles Sure Shot Questions
CBSE Class 10 Mathematics Case Studies
CBSE Class 10 Statistics Sure Shot Questions Set D
z More Study Material Class 10 Mathematics
Class 10 Mathematics All Chapters Test Paper Solved
~ Class 10 Mathematics (Old Chapters)
CBSE Class 10 Constructions Important Formulas and concepts for exams
CBSE Class 10 Constructions Sure Shot Questions

Important Practice Resources for Class 10 Mathematics

CBSE Class 10 Mathematics Chapter 7 Coordinate Geometry Study Material

Students can find all the important study material for Chapter 7 Coordinate Geometry on this page. This collection includes detailed notes, Mind Maps for quick revision, and Sure Shot Questions that will come in your CBSE exams. This material has been strictly prepared on the latest 2026 syllabus for Class 10 Mathematics. Our expert teachers always suggest you to use these tools daily to make your learning easier and faster.

Chapter 7 Coordinate Geometry Expert Notes & Solved Exam Questions

Our teachers have used the latest official NCERT book for Class 10 Mathematics to prepare these study material. We have included previous year examination questions and also step-by-step solutions to help you understand the marking scheme too. After reading the above chapter notes and solved questions also solve the practice problems and then compare your work with our NCERT solutions for Class 10 Mathematics.

Complete Revision for Mathematics

To get the best marks in your Class 10 exams you should use Mathematics Sample Papers along with these chapter notes. Daily practicing with our online MCQ Tests for Chapter 7 Coordinate Geometry will also help you improve your speed and accuracy. All the study material provided on studiestoday.com is free and updated regularly to help Class 10 students stay ahead in their studies and feel confident during their school tests.

What is included in the advanced study material for Class 10 Mathematics Chapter Chapter 7 Coordinate Geometry?

Our advanced study package for Chapter Chapter 7 Coordinate Geometry includes detailed concepts, diagrams, Mind Maps, and explanation of complex topics to ensure Class 10 students learn as per syllabus for 2026 exams.

How do Mind Maps for Mathematics Chapter Chapter 7 Coordinate Geometry help in revision?

The Mind Maps provided for Chapter Chapter 7 Coordinate Geometry act as visual anchors which will help faster recall during high-pressure exams.

Are these Mathematics resources suitable for both classroom teaching and self-study?

Yes, teachers use our Class 10 Mathematics resources for lesson planning as they are in simple language and have lot of solved examples.

Is this advanced study material for Chapter Chapter 7 Coordinate Geometry free to download in PDF?

Yes, You can download the complete, mobile-friendly PDF of the Mathematics Chapter Chapter 7 Coordinate Geometry advanced resources for free.

Does this material cover rationalized content for the 2025-26 CBSE session?

Yes, our subject matter experts have updated the Chapter Chapter 7 Coordinate Geometry material to align with the rationalized NCERT textbooks and have removed deleted topics and added new competency-based questions.