MathsMCQ Questions for Class 10 Maths Coordinate Geometry with Answers

MCQ Questions for Class 10 Maths Coordinate Geometry with Answers

Class 10 Maths MCQs Chapter 7 Coordinate Geometry

1. The distance of the point P(2, 3) from the x-axis is
(a) 2
(b) 3
(c) 1
(d) 5

Answer/ Explanation

Answer: b
Explanation: Reason: The distance from x-axis is equal to its ordinate i.e., 3

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    2. The distance between the point P(1, 4) and Q(4, 0) is
    (a) 4
    (b) 5
    (c) 6
    (d) 3√3

    Answer/ Explanation

    Answer: b
    Explanation: Reason: The required distance = \(\sqrt{(4-1)^{2}+(0-4)^{2}}=\sqrt{9+16}=\sqrt{25}=5\)


    3. 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/ Explanation

    Answer: d
    Explanation: Reason: The points are collinear if area of Δ = 0
    = \(\frac{1}{2}\)[-5(p + 2) +l(-2 -1) + 4(1 – p)] – 0
    ⇒ -5 p -10-3 + 4-4p = 0
    ⇒ -9p = +9
    ∴ p = -1


    4. 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/ Explanation

    Answer: c
    Explanation: Reason: Area of ΔABC = \(\frac{1}{2}\) [x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)] = \(\frac{1}{2}\)[-5(-5 – 5) -4(5 – 7) + 4(7 – (-5))] = \(\frac{1}{2}\)[-5(-10) -4(-2) + 4(12)] = \(\frac{1}{2}\)[50 + 8 + 48] = \(\frac{1}{2}\) × 106 = 53 sq. units


    5. The distance of the point (α, β) from the origin is
    (a) α + β
    (b) α² + β²
    (c) |α| + |β|
    (d) \(\sqrt{\alpha^{2}+\beta^{2}}\)

    Answer/ Explanation

    Answer: d
    Explanation: Reason: Distance of (α, β) from origin (0, 0) = \(\sqrt{(\alpha-0)^{2}+(\beta-0)^{2}}=\sqrt{\alpha^{2}+\beta^{2}}\)


    6. 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/ Explanation

    Answer: a
    Explanation: Reason: Required area= \(\frac{1}{2}\)[1(3 + 4) -2(-4 – 2) -3(2 – 3)] = \(\frac{1}{2}\)[7 + 12 + 3] = \(\frac{1}{2}\) × 22 = 11


    7. 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/ Explanation

    Answer: b
    Explanation: Reason: Since the line segment AB is trisected
    MCQ Questions for Class 10 Maths Coordinate Geometry with Answers 1


    8. 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/ Explanation

    Answer: a
    Explanation: Reason: Let the line 3x + y – 9 = 0 divide the line segment joining A(l, 3) ad B(2, 7) in the ratio K : 1 at point C.
    MCQ Questions for Class 10 Maths Coordinate Geometry with Answers 2


    9. The distance between A (a + b, a – b) and B(a – b, -a – b) is

    Answer/ Explanation

    Answer: c
    Explanation:
    MCQ Questions for Class 10 Maths Coordinate Geometry with Answers 3


    10. If (a/3, 4) is the mid-point of the segment joining the points P(-6, 5) and R(-2, 3), then the value of ‘a’ is
    (a) 12
    (b) -6
    (c) -12
    (d) -4

    Answer/ Explanation

    Answer: c
    Explaination:
    MCQ Questions for Class 10 Maths Coordinate Geometry with Answers 4


    11. 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/ Explanation

    Answer: d
    Explanation: Reason: We have \(\sqrt{(x-3)^{2}+(-1-2)^{2}}=5\)
    ⇒ (x – 3)² + 9 = 25
    ⇒ x² – 6x + 9 + 9 = 25
    ⇒ x² -6x – 7 = 0
    ⇒ (x – 7)(x + 1) = 0
    ⇒ x = 7 or x = -1


    12. 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/ Explanation

    Answer: b
    Explanation: Reason: Let A(1, 1), B(-2, 7) and C(3, 3) are the given points, Then, we have
    MCQ Questions for Class 10 Maths Coordinate Geometry with Answers 5


    13. 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/ Explanation

    Answer: d
    Explanation: Reason: The co-ordinates of the centroid of the triangle is
    MCQ Questions for Class 10 Maths Coordinate Geometry with Answers 6

     


    14. 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/ Explanation

    Answer: c
    Explanation: Reason: Let the coordinates of the third vertex be (x, y)
    MCQ Questions for Class 10 Maths Coordinate Geometry with Answers 7

     


    15. 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/ Explanation

    Answer: a
    Explanation: Reason: Area of ΔABC = \(\frac{1}{2}\) [-1.5(-2 – 4) + 6(4 – 3) + (-3) (3 + 2)] = \(\frac{1}{2}\) [9 + 6 – 15] = 0. It is a straight line.


    16. 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/ Explanation

    Answer: a
    Explanation: Reason: Area of ΔPBC = 0
    ⇒ \(\frac{1}{2}\)[1(0 – b) + 0(6 – 1) + a(2 – 0)] = 0
    ⇒ \(\frac{1}{2}\)[-6 + 2a] = 0
    ⇒ -b + 2a = 0
    ∴ 2a = b


    We hope the given MCQ Questions for Class 10 Maths Coordinate Geometry with Answers will help you. If you have any query regarding CBSE Class 10 Maths Chapter 7 Coordinate Geometry Multiple Choice Questions with Answers, drop a comment below and we will get back to you at the earliest.

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