MCQs for Class 10 Maths Chapter 7 Coordinate Geometry
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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) √(α2+β2)
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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