# MCQs for Class 10 Maths Chapter 7 Coordinate Geometry

MCQs for **Class 10 Maths Chapter 7 Co-Ordinate Geometry**: In this article, we have covered all the important MCQs for Free for Class 10 Term 1 2021-22 Board Exams. In accordance with the latest pattern, Padhle is here with MCQ Questions for Class 10.

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# MCQs for Class 10 Maths Chapter 7 Co-Ordinate Geometry

1. The distance of the point P(2, 3) from the x-axis is

(a) 2

(b) 3

(c) 1

(d) 5

Answer: b

2. If the distance between the points (2, –2) and (–1, x) is 5, one of the values of x is

(a) –2

(b) 2

(c) –1

(d) 1

Answer: (b) 2

3. The points (- 1, – 2), (1, 0), (- 1, 2), (- 3, 0) forms a quadrilateral of type:

(a)Square

(b)Rectangle

(c)Parallelogram

(d)Rhombus

Answer: (a) square

4. The distance between the points A(0, 6) and B(0, -2) is

(a) 6

(b) 8

(c) 4

(d) 2

Answer: (b) 8

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5.The distance between the point P(1, 4) and Q(4, 0) is

(a) 4

(b) 5

(c) 6

(d) 3√3

Answer: (b) 5

6. Find the coordinates of the point equidistant from the points A(1, 2), B (3, –4) and C(5, –6).

(a) (2, 3)

(b) (–1, –2)

(c) (0, 3)

(d) (1, 3)

Answer: (b) (–1, –2)

7. The area of triangle whose vertices are (1,-1), (-4.6), and (-3, -5) is

(a) 21

(b) 32

(c) 24

(d) 25

Answer: (c) 24

8. The points (-5, 1), (1, p) and (4, -2) are collinear if the value of p is

(a) 3

(b) 2

(c) 1

(d) -1

Answer: (d) -1

9. The distance between the point P(1, 4) and Q(4, 0) is

(a) 4

(b) 5

(c) 6

(d) 3√3

Answer: (b) 5

10. The mid-point of the line segment joining the points A (–2, 8) and B (– 6, – 4) is

(a) (– 4, – 6)

(b) (2, 6)

(c) (– 4, 2)

(d) (4, 2)

Answer: (c) (– 4, 2)

11. The midpoints of a line segment joining two points A(2, 4) and B(-2, -4)

(a) (-2,4)

(b) (2,-4)

(c) (0, 0)

(d) (-2,-4)

Answer: (c) (0, 0)

12. The distance of the point P(-6, 8) from the origin is

(a) 8

(b) 2√7

(c) 10

(d) 6

Answer: (c) 10

13. The area of the triangle whose vertices are A(1, 2), B(-2, 3) and C(-3, -4) is

(a) 11

(b) 22

(c) 33

(d) 21

Answer: (a) 11

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14. Find the coordinates of the point equidistant from the points A(5, 1), B(–3, –7) and C(7, –1).

(a) (2, –4)

(b) (3, –6)

(c) (4, 7)

(d) (8, –6)

Answer: (a) (2, –4)

15. If the area of a quadrilateral ABCD is zero, then the four points A, B, C, D are

(a) Collinear

(b) Not collinear

(c) Nothing can be said

(d) None of these

Answer: (a) Collinear

16. The area of the triangle ABC with the vertices A(-5, 7), B(-4, -5) and C(4, 5) is

(a) 63

(b) 35

(c) 53

(d) 36

Answer: (c) 53

17. The points (-5, 1), (1, p) and (4, -2) are collinear if the value of p is

(a) 3

(b) 2

(c) 1

(d) -1

Answer: (d) -1

18. The points A (9, 0), B (9, 6), C (–9, 6) and D (–9, 0) are the vertices of a

(a) Square

(b) Rectangle

(c) Rhombus

(d) Trapezium

Answer: (b) Rectangle

19. The distance between the points P(0, 2) and Q(6, 0) is

(a)4√10

(b)2√10

(c)√10

(d)20

Answer: (b)2√10

20. The distance between the points (0, 5) and (-5, 0) is

(a) 5

(b) 5√2

(c) 2√5

(d) 10

Answer: (b) 5√2

21. The coordinates of the centre of a circle passing through (1, 2), (3, – 4) and (5, – 6) is:

(a) (11, – 2)

(b) (-2, 11)

(c) (11, 2)

(d) (2, 11)

Answer: (c) (11, 2)

22. Find the value of P for which the point (–1, 3), (2, p) and (5, –1) are collinear.

(a) 4

(b) 3

(c) 2

(d) 1

Answer: (d) 1

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23. If (1,2), (4,y), (x,6), and (3,5) are the vertices of a parallelogram taken in order. Then (x,y) is

(a) (6, 2)

(b) (6, 3)

(c) (6, 4)

(d) (3, 4)

Answer: (b) (6, 3)

24. If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is

(a) -7 or -1

(b) -7 or 1

(c) 7 or 1

(d) 7 or -1

Answer: (d) 7 or -1

25. The area of the triangle ABC with the vertices A(-5, 7), B(-4, -5) and C(4, 5) is

(a) 63

(b) 35

(c) 53

(d) 36

Answer: (c) 53

26. The distance of the point P (2, 3) from the x-axis is

(a) 2

(b) 3

(c) 1

(d) 5

Answer: (b) 3

27. .If O(p/3, 4) is the midpoint of the line segment joining the points P(-6, 5) and Q(-2, 3). The value of p is:

(a)7/2

(b)-12

(c)4

(d)-4

Answer: (b)-12

28. AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is

(a) 5

(b) 3

(c) √34

(d) 4

Answer: (c) √34

29. The distance of the point (– 3, 4) from the origin is

(a) 25 units

(b) 1 unit

(c) 7 units

(d) 5 units

Answer: (d) 5 units

30. Find the distance of the point (–6, 8) from the origin.

(a) 8

(b) 11

(c) 10

(d) 9

Answer: (c) 10

31. The coordinates of a point A, where AB is the diameters of a circle whose centre (2,-3) and B is (1,4) is

(a) (3, -9)

(b) (2, 9)

(c) (3, -10)

(d) (4, 5)

Answer: (c) (3, -10)

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32. The area of the triangle formed by the points A(-1.5, 3), B(6, -2) and C(-3, 4) is

(a) 0

(b) 1

(c) 2

(d) 3/2

Answer: (a) 0

33. The distance of the point (α, β) from the origin is

(a) α + β

(b) α² + β²

(c) |α| + |β|

(d) √(α^{2}+β^{2})

Answer: (d) √(α2+β2)

34. The distance between the points A (0, 6) and B (0, –2) is

(a) 6

(b) 8

(c) 4

(d) 2

Answer: (b) 8

35. The points which divides the line segment of points P(-1, 7) and (4, -3) in the ratio of 2:3 is:

(a)(-1, 3)

(b)(-1, -3)

(c)(1, -3)

(d)(1, 3)

Answer: (d)(1, 3)

36. The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is

(a) 5

(b) 12

(c) 11

(d) 7 + √5

Answer: (b) 12

37. The distance of the point P (2, 3) from the x-axis is

(a) 2

(b) 3

(c) 1

(d) 5

Answer: (b) 3

38. Find the value of p for which the points (–5, 1), (1, p) and (4, –2) are collinear.

(a) –3

(b) –2

(c) 0

(d) –1

Answer: (d) –1

39. Let P(x, y) be equidistant from the points A (7, 1) and (3, 5).Find a relation between x and y.

(a) y – x = 4

(b) y – x = 2

(c) x – y = 2

(d) x – y = 4

Answer: (c) x – y = 2

40. If the points P(1, 2), B(0, 0) and C(a, b) are collinear, then

(a) 2a = b

(b) a = -b

(c) a = 2b

(d) a = b

Answer: (a) 2a = b

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41. The line segment joining the points (3, -1) and (-6, 5) is trisected. The coordinates of point of trisection are

(a) (3, 3)

(b) (- 3, 3)

(c) (3, – 3)

(d) (-3,-3)

Answer: (b) (- 3, 3)

42. If P (a/3, 4) is the mid-point of the line segment joining the points Q (– 6, 5) and R (– 2, 3), then the value of a is

(a) – 4

(b) – 12

(c) 12

(d) – 6

Answer: (b) – 12

43. The ratio in which the line segment joining the points P(-3, 10) and Q(6, – 8) is divided by O(-1, 6) is:

(a)1:3

(b)3:4

(c)2:7

(d)2:5

Answer: (c)2:7

44. The area of a triangle with vertices A(3, 0), B(7, 0) and C(8, 4) is

(a) 14

(b) 28

(c) 8

(d) 6

Answer: (c) 8

45. The distance between the points (a, a) and (−√3a,√3a) is

(a) 3√2a units

(b) 2√2a units

(c) 2√2 units

(d) 2 units

Answer: (b) 2√2a units

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

(a) 2

(b) 3

(c) 0

(d) 1

Answer: (c) 0

47. The coordinates of the point which divides the line segment joining points A(5,-2) and B(9,6) in the ratio 3:1 are

(a) (-4,3)

(b) (5,-6)

(c) (8,4)

(d) (0,7)

Answer: (c) (8,4)

48. If the segment joining the points (a, b) and (c, d) subtends a right angle at the origin, then

(a) ac – bd = 0

(b) ac + bd = 0

(c) ab + cd = 0

(d) ab – cd= 0

Answer: (b) ac + bd = 0

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49. The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally in the ratio

(a) 3 : 4

(b) 3 : 2

(c) 2 : 3

(d) 4 : 3

Answer: (a) 3 : 4

50. If the distance between the points (4, p) and (1, 0) is 5, then the value of p is

(a) 4 only

(b) ± 4

(c) – 4 only

(d) 0

Answer:(b) ± 4

51.The coordinates of a point P, where PQ is the diameter of circle whose centre is (2, – 3) and Q is (1, 4) is:

(a)(3, -10)

(b)(2, -10)

(c)(-3, 10)

(d)(-2, 10)

Answer: (a)(3, -10)

52. The points (-4, 0), (4, 0), (0, 3) are the vertices of a

(а) Right triangle

(b) Isosceles triangle

(c) Equilateral triangle

(d) Scalene triangle

Answer: (b) Isosceles triangle

53. The mid-point of the line segment joining the points A (-2, 8) and B (-6, -4) is

(a) (-4, -6)

(b) (2, 6)

(c) (-4, 2)

(d) (4, 2)

Answer: (c) (-4, 2)

54. In what ratio of line x – y – 2 = 0 divides the line segment joining (3, –1) and (8, 9)?

(a) 1 : 2

(b) 2 : 1

(c) 2 : 3

(d) 1 : 3

Answer: (c) 2 : 3

55. The co-ordinates of the points which divides the join of (– 2, – 2) and (– 5, 7) in the ratio 2 : 1 is :

(a) (4, – 4)

(b) (– 3, 1)

(c) (– 4, 4)

(d) (1, – 3)

Answer: (c) (– 4, 4)

56. The points (1,1), (-2, 7) and (3, -3) are

(a) vertices of an equilateral triangle

(b) collinear

(c) vertices of an isosceles triangle

(d) none of these

Answer: (b) collinear

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57. The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the

(a) I quadrant

(b) II quadrant

(c) III quadrant

(d) IV quadrant

Answer: (d) IV quadrant

58. he area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2,-1) taken in order, is:

(a)12 sq.unit

(b)24 sq.unit

(c)30 sq.unit

(d)32 sq.unit

Answer: (b)24 sq.unit

59. The fourth vertex D of a parallelogram ABCD whose three vertices are A(-2, 3), B(6, 7) and C(8, 3) is

(a) (0, 1)

(b) (0, -1)

(c) (-1, 0)

(d)(1, 0)

Answer: (b) (0, -1)

60. The area of the triangle formed by joining the mid-points of the sides of the triangle, whose vertices are (0, -1), (2, 1) and (0, 3) is

(a) 4

(b) 2

(c) 3

(d) 1

Answer: (d) 1

61. The vertices of a ΔABC and given by A(2, 3) and B(–2, 1) and its centroid is G (1 ½) Find the coordinates of the third vertex C of the ΔABC.

(a) (0, 2)

(b) (1, –2)

(c) (2, –3)

(d) (–2, 3)

Answer: (d) (–2, 3)

62. The distance between the points P (-6,7) and Q (-1,-5) is

(a) 15

(b) 12

(c) 13

(d) 10

Answer: (c) 13

63. The coordinates of the centroid of a triangle whose vertices are (0, 6), (8,12) and (8, 0) is

(a) (4, 6)

(b) (16, 6)

(c) (8, 6)

(d) (16/3, 6)

Answer: (d) (16/3, 6)

64. One of the two points of trisection of the line segment joining the points A (7, – 2) and B (1, – 5) which divides the line in the ratio 1:2 are:

(a) (5, –3)

(b) (5, 3)

(c) (–5, –3)

(d) (13, 0)

Answer: (a) (5, –3)

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65. If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then

(a) AP = 1/3 AB

(b) AP = PB

(c) PB = 1/3 AB

(d) AP = 1/2 AB

Answer: (d) AP = 1/2 AB

66. The ordinate of a point is twice its abscissa. If its distance from the point (4,3) is √10, then the coordinates of the point are

(a) (1,2) or (3,6)

(b) (1,2) or (3,5)

(c) (2,1) or (3,6)

(d) (2,1) or (6,3)

Answer: (a) (1,2) or (3,6)

67. Find the ratio in which the line joining the points (6, 4) and (1, –7) is divided by x-axis.

(a) 1 : 3

(b) 2 : 7

(c) 4 : 7

(d) 6 : 7

Answer: (c) 4 : 7

68. The coordinates of the centre of a circle are (– 6, 1.5). If the ends of a diameter are (– 3, y) and (x, – 2) then:

(a) x = – 9, y = 5

(b) x = 5, y = – 9

(c) x = 9, y = 5

(d) None of these

Answer: (a) x = – 9, y = 5

69. Two vertices of a triangle are (3, – 5) and (- 7,4). If its centroid is (2, -1), then the third vertex is

(a) (10, 2)

(b) (-10,2)

(c) (10,-2)

(d) (-10,-2)

Answer: (c) (10,-2)

70. A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2, –5) is the mid – point of PQ, then the coordinates of P and Q are, respectively.

(a) (0, – 5) and (2, 0)

(b) (0, 10) and (– 4, 0)

(c) (0, 4) and (– 10, 0)

(d) (0, – 10) and (4, 0)

Answer: (d) (0, – 10) and (4, 0)

71. If P (α3, 4) is the mid-point of the line segment joining the points Q(-6, 5) and R(-2, 3), then the value of‘a’ is

(a) -4

(b) -12

(c) 12

(d) -6

Answer: (b) -12

72. If (a, 0) , (0, b) and (x, y) are collinear, then

(a) ay + bx = ab

(b) ax + by = 1

(c) ax – by = ab

(d) ay – bx = 1

Answer: (a) ay + bx = ab

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73. The graph of the equation x = 3 is:

(a) a point

(b) straight line parallel to y axis

(c) straight line passing through the origin

(d) straight line parallel to x axis

Answer: (b) straight line parallel to y axis

74. The horizontal and vertical lines drawn to determine the position of a point in a Cartesian plane are called

(a) Intersecting lines

(b) Transversals

(c) Perpendicular lines

(d) X-axis and Y-axis

Answer: (d) X-axis and Y-axis

75. he line segment joining (2, – 3) and (5, 6) is divided by x-axis in the ratio:

(a) 2 : 1

(b) 3 : 1

(c) 1 : 2

(d) 1 : 3

Answer: (a) 2 : 1

76. If A and B are the points (-6, 7) and (-1, -5) respectively, then the distance 2AB is equal to

(a) 26

(b) 169

(c) 13

(d) 238

Answer: (a) 26

77. Three consecutive vertices of a parallelogram are (1, –2), (3, 6) and (5, 10). The coordinates of the fourth vertex are :

(a) (–3, 2)

(b) (2, – 3)

(c) (3, 2)

(d) (–2, –3)

Answer: (c) (3, 2)

78. The distance between the points (3,4) and (8,-6) is

(a) 2√5 units

(b) 3√5 units

(c) √5 units

(d) 5√5 units

Answer: (d) 5√5 units

79. The perimeter of the triangle formed by the points A(0,0), B(1,0) and C(0,1) is

(a) √2 + 1

(b) 1 ± √2

(c) 2 + √2

(d) 3

Answer: (c) 2 + √2

80. The values of x and y, if the distance of the point (x,y) from (-3,0) as well as from (3,0) is 4 are

(a) x = 1, y = 7

(b) x = 2, y = 7

(c) x = 0, y = – √7

(d) x = 0, y = ± √7

Answer: (d) x = 0, y = ± √7

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