CBSE Class 10 Coordinate geometry Sure Shot Questions Set A

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Study Material for Class 10 Mathematics Chapter 7 Coordinate Geometry

Class 10 Mathematics students should refer to the following Pdf for Chapter 7 Coordinate Geometry in Class 10. These notes and test paper with questions and answers for Class 10 Mathematics will be very useful for exams and help you to score good marks

Class 10 Mathematics Chapter 7 Coordinate Geometry

 

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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 Linear Equations
CBSE Class 10 Pair of linear equations Important Formulas and concepts for exams
CBSE Class 10 Pair of Linear Equations Sure Shot Questions Set A
CBSE Class 10 Pair of Linear Equations Sure Shot Questions Set B
CBSE Class 10 Pair of Linear Equations Sure Shot Questions Set C
CBSE Class 10 Pair of Linear Equations 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
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
Chapter 10 Circles
CBSE Class 10 Circles Important Formulas and concepts for exams
CBSE Class 10 Circles Sure Shot Questions
Chapter 11 Constructions
CBSE Class 10 Constructions Important Formulas and concepts for exams
CBSE Class 10 Constructions Sure Shot Questions
Chapter 13 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
Chapter 14 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 15 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
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

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CBSE Class 10 Mathematics Chapter 7 Coordinate Geometry Study Material

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