CBSE Class 10 Coordinate geometry Sure Shot Questions Set B

CBSE Class 10 Coordinate geometry Sure Shot Questions Set B. 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 coordinates of the point which divides the line segment joining the points A(4, –3) and B(9, 7) in the ration 3 : 2.

2. Find the coordinates of the point which divides the line segment joining the points A(–1, 7) and B(4, –3) in the ration 2 : 3.

3. Find the coordinates of the point which divides the line segment joining the points A(–5, 11) and B(4, –7) in the ration 7 : 2.

4. Find the coordinates of the midpoint of the line segment joining the points A(–5, 4) and B(7, –8)

5. Find the coordinates of the midpoint of the line segment joining the points A(3, 0) and B(5, 4)

6. Find the coordinates of the midpoint of the line segment joining the points A(–11, –8) and B(8, – 2).

7. The coordinates of the midpoint of the line segment joining the points A(2p + 1, 4) and B(5, q–1) are(2p, q). Find the value of p and q.

8. The midpoint of the line segment joining A(2a, 4) and B(–2, 3b) is M(1, 2a + 1). Find the values of a and b.

9. Find the coordinates of the points which divide the line segment joining the points (–2, 0) and (0, 8) in four equal parts.

10. Find the coordinates of the points which divide the line segment joining the points (–2, 2) and (2, 8) in four equal parts.

11. In what ratio does the points P(2,–5) divide the line segment joining A(–3, 5) and B(4, –9).

12. In what ratio does the points P(2, 5) divide the line segment joining A(8, 2) and B(–6, 9).

13. Find the coordinates of the points of trisection of the line segment joining the points (4, –1) and (–2, –3).

14. The line segment joining the points (3, –4) and (1, 2) is trisected at the points P(p, –2) and Q( 5 /3,q). Find the values of p and q.

15. The coordinate of the midpoint of the line joining the point (3p, 4) and (–2, 2q) are (5, p). Find the value of p and q.

16. The consecutive vertices of a parallelogram ABCD are A(1, 2), B(1, 0) and C(4, 0). Find the fourth vertex D.

17. Find the lengths of the median of the triangle whose vertices are (1, –1), (0, 4) and (–5, 3).

18. Prove that the diagonal of a rectangle bisects each other and are equal.

19. Find the ratio in which the point (11, 15) divides the line segment joining the point (15, 5) and (9, 20).

20. Find the ratio in which the point P(m, 6) divides the line segment joining the point A(–4, 3) and B(2, 8). Also find the value of m.

21. If two vertices of △ABC are A(3, 2), B(–2, 1) and its centroid G has the coordinate (5/3, –1/3). Find the coordinates of the third vertex.

22. The coordinate of the midpoint of the line joining the point (2p, 4) and (–2, 2q) are (3, p). Find the value of p and q.

23. Show that the points A(3, 1), B(0, –2), C(1, 1) and D(4, 4) are the vertices of a parallelogram ABCD.

24. If the points P(a, –11), Q(5, b), R(2, 15) and S(1, 1) are the vertices of a parallelogram PQRS, find the value of a and b.

25. If three consecutive vertices of a parallelogram ABCD are A(1, –2), B(3, 6) and C(5, 10). Find the fourth vertex D.

26. In what ratio does the point (– 4, 6) divide the line segment joining the points A(– 6, 10) and B(3, – 8)?

27. Find the coordinates of the points of trisection of the line segment joining the points A(2, – 2) and B(– 7, 4).

28. Find the ratio in which the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4). Also find the point of intersection.

29. 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.

30. If the points A(–2, –1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram, taken in order, find the value of a and b.

31. Find the ratio in which the point P(–6, a) divides the join of A(–3, –1) and B(–8, 9). Also, find the value of a.

32. Find the ratio in which the point P(–3, a) divides the join of A(–5, –4) and B(–2, 3). Also, find the value of a.

33. Find the ratio in which the point P(a, 1) divides the join of A(–4, 4) and B(6, –1). Also, find the value of a.

34. Find the ratio in which the line segment joining the points (– 3, 10) and (6, – 8) is divided by (– 1, 6).

35. Find the ratio in which the line segment joining A(1, – 5) and B(– 4, 5) is divided by the x-axis. Also find the coordinates of the point of division.

36. In what ratio is the line segment joining A(6, –3) and B(–2, –5) is divided by the x-axis. Also find the coordinates of the point of intersection of AB and the x-axis. Prepared by: M. S. KumarSwamy, TGT(Maths)

37. In what ratio is the line segment joining A(2, –3) and B(5, 6) is divided by the x-axis. Also find the coordinates of the point of intersection of AB and the x-axis.

38. In what ratio is the line segment joining A(–2, –3) and B(3, 7) is divided by the y-axis. Also find the coordinates of the point of intersection of AB and the y-axis.

39. The coordinates of one end point of a diameter AB of a circle are A(4, –1) and the coordinates of the centre of the circle are C(1, –3).

40. Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, – 3) and B is (1, 4).

41. The line segment joining A(–2, 9) and B(6, 3) is a diameter of a circle with centre C. Find the coordinates of C.

42. AB is a diameter of a circle with centre C(–1, 6). If the coordinates of A are (–7, 3), find the coordinates of B.

43. Find the ratio in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2, – 2) and B(3, 7).

44. Find the ratio in which the line x – y – 2 = 0 divides the line segment joining the points A(3, –1) and B(8, 9).

45. Find the ratio in which the line 3x + 4y – 9 = 0 divides the line segment joining the points A(1, 3) and B(2, 7).

46. Find the lengths of the medians of a triangle ABC whose vertices are A(7, –3), B(5, 3) and C(3, –1).

47. Find the lengths of the medians of a triangle ABC whose vertices are A(0, –1), B(2, 1) and C(0,3).

48. Let D(3, –2), E(–3, 1) and F(4, –3) be the midpoints of the sides BC, CA and AB respectively of △ABC. Then, find the coordinates if the vertices A, B and C.

49. If A and B are (– 2, – 2) and (2, – 4), respectively, find the coordinates of P such that AP = 3/7 AB and P lies on the line segment AB.

50. A(1, 1) and B(2, –3) are two points. If C is a point lying on the line segment AB such that CB = 2AC, find the coordinates of C

51. If A(1, 1) and B(–2, 3) are two points and C is a point on AB produced such that AC = 3AB, find the coordinates of C.

52. Find the coordinates of the point P which is three-fourth of the way from A(3, 1) to B(–2, 5).

53. The line joining the points A(4, –5) and B(4, 5) is divided by the point P such that AP : AB = 2 : 5, find the coordinates of P.

54. The point P(–4, 1) divides the line segment joining the points A(2, –2) and B in the raio 3 : 5. Find the point B. Prepared by: M. S. KumarSwamy, TGT(Maths)

55. If A and B are (4, –5) and (4, 5), respectively, find the coordinates of P such that AP = 2/5AB and P lies on the line segment AB.

56. Find the coordinates of the points of trisection of the line segment AB, whose end points are A(2, 1) and B(5, –8).

57. Find the coordinates of the points which divide the join A(–4, 0) and B(0, 6) in three equal parts.

58. The line joining the points A(2, 1) and B(5, –8) is trisected at the points P and Q. If the point P lies on the line 2x – y + k = 0, find the value of k.

59. Find the coordinates of the points which divide the line segment joining A(– 2, 2) and B(2, 8) into four equal parts.

60. If A(5, –1), B(–3, –2) and C(–1, 8) are the vertices of △ABC, find the length of the median through A and the coordinates of the centroid.

61. Find the centroid of △ABC whose vertices are vertices are A(–3, 0), B(5, –2) and C(–8, 5).

62. Two vertices of a △ABC are given by A(6, 4) and B(–2, 2) and its centroid is G(3, 4). Find the coordinates of the third vertex C of △ABC.

63. Find the coordinates of the centroid of a △ABC whose vertices are A(6, –2), B(4, –3) and C(–1, –4).

64. Find the centroid of a △ABC whose vertices are A(–1, 0), B(5, –2) and C(8, 2).

65. A(3, 2) and B(–2, 1) are two vertices of a △ABC, whose centroid is G( 5/3 , 1/3). Find the coordinates of the third vertex C.

66. If G(–2, 1) is the centroid of △ABC and two of its vertices are A(1, –6) and B(–5, 2), find the third vertex of the triangle.

67. Find the third vertex of a △ABC if two of its vertices are B(–3, 1) and C(0, –2) and its centroid is at the origin.

68. The line segment joining A(–1, 5/3) and B(a, 5) is divided in the ratio 1 : 3 at P, the point where the line segment AB intersects y-axis. Find the value of a and the coordinates of P.

69. Find the ratio in which the point P whose ordinate is –3 divides the join of A(–2, 3) and B(5, -15/2). Hence find the coordinate of P.

70. Calculate the ratio in which the line joining the points A(6, 5) and B(4, –3) is divided by the line y = 2. Also, find the coordinates of the point of intersection.

71. Show that the points (3, –2), (5, 2) and (8, 8) are collinear by using section formula. Prepared by: M. S. KumarSwamy, TGT(Maths)

72. If the points (–1, –1), (2, p) and (8, 11) are collinear, find the value of p using section formula.

73. If the points (2, 3), (4, k) and (6, –3) are collinear, find the value of k using section formula.

74. If two vertices of a parallelogram are (3, 2), (–1, 0) and its diagonals meet at (2, –5), find the other two vertices of the parallelogram.

75. Find the coordinates of the vertices of a triangle whose midpoints are (–3, 2), (1, –2) and (5, 6).

76. Find the third vertex of a triangle if its two vertices are (–1, 4) and (5, 2) and midpoint of one side is (0, 3).

77. If the midpoints of the sides of a triangle are (2, 3), ( 3/2, 4) and ( 11/2, 5), find the centroid of the triangle.

78. If the points (10, 5), (8, 4) and (6, 6) are the midpoints of the sides of a triangle, find its vertices.

79. If the point C(–1, 2) divides the line segment AB in the ratio 3 : 4, where the coordinates of A are (2, 5), find the coordinates of B.

80. The vertices of a quadrilateral are (1, 4), (–2, 1), (0, –1) and (3, 2). Show that diagonals bisect each other. What does quadrilateral become?

81. Using analytical geometry, prove that the midpoint of the hypotenuse of a right triangle is equidistant from its vertices.

82. Using analytical geometry, prove that the diagonals of a rhombus are perpendicular to each other.

83. Prove analytically that the line segment joining the midpoint of two sides of a triangle is half of the third side.

84. If (–2, 3), (4, –3) and (4, 5) are the midpoints of the sides of a triangle, find the coordinates of its centroid.

85. If (1, 1), (2, –3) and (3, 4) are the midpoints of the sides of a triangle, find the coordinates of its centroid.

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