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.
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