CBSE Class 10 Mathematics Coordinate Geometry MCQs Set 04

Question. If the mid – point of the line segment joining the points (a, b – 2) and ( – 2, 4) is (2, – 3), then the values of ‘a’ and ‘b’ are
(a) 6, 8
(b) 6, – 8
(c) 4, – 5
(d) – 6, 8

Answer: B

Question. The vertices of a quadrilateral are (1, 7), (4, 2), ( – 1, – 1) and ( – 4, 4). The quadrilateral is a
(a) rectangle
(b) parallelogram
(c) square
(d) Rhombus

Answer: C

Question. The centroid of a triangle whose vertices are (3, -7), ( -8, 6) and (5, 10) is
(a) (0, 3)
(b) (1, 3)
(c) (3, 3)
(d) (0, 9)

Answer: A

Question. The points A(1, 2), B(5, 4), C(3, 8) and D( – 1, 6) are the vertices of a
(a) Rectangle
(b) Rhombus
(c) Square
(d) Parallelogram

Answer: C

Question. The coordinates of the point which is reflection of point (–3, 5) in x-axis are
(a) (3, 5)
(b) (3, –5)
(c) (–3, –5)
(d) (–3, 5)

Answer: C

Question. The point P on x-axis equidistant from the points A(–1, 0) and B(5, 0) is
(a) (2, 0)
(b) (0, 2)
(c) (3, 0)
(d) (2, 2)

Answer: A

Question. The value(s) of y, if the distance between the points (2, y) and (– 4, 3) is 10, is
(a) 11
(b) –5
(c) Both
(a) and (b)
(d) None of the options

Answer: C

Question. The points (a, a), (–a, –a) and (− √3a, √3a) are the vertices of a/an
(a) Equilateral triangle
(b) Isosceles triangle
(c) Scalene triangle
(d) None of the options

Answer: A

Question. If the distance between the points (4, k) and (1, 0) is 5, then what can be the possible values of k?
(a) k = 4
(b) k = –4
(c) k = ± 4
(d) None of the options

Answer: C

Question. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, x and y respectively are
(a) x = 6, y = 3
(b) x = 3, y = 6
(c) x = –6, y = –3
(d) x = –3, y = –6

Answer: A

Question. The distance between the points (a cos θ + b sin θ , 0) and (0, a sin θ – b cos θ), is
(a) a² + b²
(b) a² – b²
(c) √a² + b²
(d) √a² − b²

Answer: C

Question. The points A(4, – 1), B(6, 0), C(7, 2) and D(5, 1) are the vertices of a
(a) Square
(b) Parallelogram
(c) Rhombus
(d) Rectangle

Answer: C

Question. If the co – ordinates of a point are ( – 5, 11), then its abscissa is
(a) -5
(b) 11
(c) 5
(d) -11

Answer: A

Question. The centre of a circle is (2a – 1, 7) and it passes through the point (–3, –1). If the diameter of the circle is 20 units, then the value of a is
(a) α = –2, 3
(b) α = 4, 2
(c) α = 5, –3
(d) α = –4, 2

Answer: D

Question. The distance of a point from the origin is
(a) x² + y² 
(b) x² – y²
(c) √x² + y²
(d) None of the options

Answer: C

Question. AOBC is a rectangle whose three vertices are A(0, –3), O(0, 0) and B(4, 0). The length of its diagonal is
(a) 3 units
(b) 5 units
(c) 7 units
(d) 9 units

Answer: B

Question. The distance between the points (3, –2) and (–3, 2) is
(a) √52 units
(b) 4√10 units
(c) 2√10 units
(d) √40 units

Answer: A

Question. If the points (x, y), (1, 2) and (7, 0) are collinear, then the relation between ‘x’ and ‘y’ is given by
(a) 3x – y – 7 = 0
(b) 3x + y + 7 = 0
(c) x + 3y – 7 = 0
(d) x – 3y + 7 = 0

Answer: C

Question. If the distance between the points (p, – 5) and (2, 7) is 13 units, then the value of ‘p’ is
(a) -3, -7
(b) 3, -7
(c) 3, 7
(d) -3, 7

Answer: D

Question. A circle has its centre at the origin and a point P(5, 0) lies on it. Then the point Q(8, 6) lies ________ the circle.
(a) in side
(b) out side
(c) on
(d) None of the options

Answer: B

Question. The point where the medians of a triangle meet is called the ________ of the triangle
(a) circumcentre
(b) centroid
(c) orthocentre
(d) None of the options

Answer: B

Question. The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, –5) and R(–3, 6), the coordinates of P are
(a) (12, 6)
(b) (8, 9)
(c) (4, 11)
(d) (16, 8)

Answer: D

Question. If points (a, 0), (0, b) and (1, 1) are collinear, then the value of 1/a + 1/b is
(a) 1
(b) 2
(c) 5
(d) 9

Answer: A

Question. Three given points will be collinear, if the area of the triangle formed by these points is
(a) 0 sq. units
(b) 1 sq. units
(c) -1 sq. units
(d) 2 sq. units

Answer: A

Question. If one end of a diameter of a circle is (4, 6) and the centre is ( – 4, 7), then the other end is
(a) ( – 12, 8)
(b) (8, – 12)
(c) (8, 10)
(d) (8, – 6)

Answer: A

Question. The value(s) of x, if the distance between the points A(0, 0) and B(x, – 4) is 5 units, is
(a) ± 2
(b) ± 3
(c) ± 4
(d) ± 5

Answer: B

Question. The value of k if the triangle formed by A(8, –10), B(7, –3) and C(0, k) is right-angled at B, is
(a) k = 2
(b) k = –2
(c) k = 4
(d) k = –4

Answer: D

Question. If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then AP is equal to
(a) AP =1/4 AB
(b) AP =1/2 AB
(c) AP =1/3 AB
(d) AP = PB

Answer: B

Question. If the points (x, y), (1, 2) and (7, 0) are collinear, then the relation between ‘x’ and ‘y’ is given by
(a) 3x – y – 7 = 0
(b) 3x + y + 7 = 0
(c) x + 3y – 7 = 0
(d) x –3y + 7 =0

Answer: C

Question. The value of a, so that the point (4, a) lies on the line 3x – 2y = 5 is
(a) 2
(b) 3
(c) 7/ 2
(d) 5/ 2

Answer: C

Question. The coordinates of the points P and Q are respectively (4, –3) and (–1, 7). The x-coordinate (abscissa) of a point R on the line segment PQ such that PQ/ PR = 5/ 3 , is
(a) 0
(b) 1
(c) 2
(d) 3

Answer: B

Question. The point on x-axis which is equidistant from the points (2, –2) and (–4, 2) is
(a) (1, 0)
(b) (2, 0)
(c) (0, 2)
(d) (–1, 0)

Answer: D

Question. The distance between the points (–5, 7) and (–1, 3) is
(a) 4 √3
(b) 4 √5
(c) 4 √2
(d) 4 √7

Answer: C

Question. In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Choose the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion (A): The point (0, 4) lies on y-axis.
Reason (R): The x-coordinate on the point on y-axis is zero.

Answer: A

Question. Assertion (A): The value of y is 6, for which the distance between the points P(2, –3) and Q(10, y) is 10.
Reason (R): Distance between two given points A (x₁, y₁) and B (x₂, y₂) is given by AB = √(x₂ – x₁)² + (y₂ – y₁)²

Answer: D

One Word Questions :

Question. Find the third vertex of a triangle, if two of its vertices are (–3, 1) and (0, –2) the centroid is at origin.
Answer: (3. 1)

Question. P is the point of x-axis such that its distance from the origin is 3 units. Find the point Q on y-axis such that OP = OQ.
Answer: (0, 3) or (0, –3)

Question. Find the third vertex of a triangle if two of its vertices are (–1, 4) and (5, 2) and centroid is (0, –3).
Answer: (–4, –15)

Question. One end of a diameter of a circle is (2, 3) and the centre is (–2, 5). What are the coordinates of the other end of his diameter?
Answer: (–6, 7)

Question. Find the coordinates of fourth vertex of the rectangle formed by the points (0, 0), (2, 0) and (0, 3).
Answer: (2, 3)

Question. What is the area of triangle ABC, whose vertices are A(x1, y1), B(x₂, y₂) and C(x₃, y₃)
Answer: 1/2 [x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃ (y₁ − y₂)]

Question. What are the coordinates of mid-point of line joining the points (6, –2) and (4, 8)?
Answer: (5, 3)

Question. Find the coordinates of a point on x-axis which is equidistant from (–2, 5) and (2, –3).
Answer: (–2, 0)

Question. What is the area of ΔABC if points A, B and C are collinear?
Answer: zero

Question. Find the sum of lengths of the diagonals AC and BD of quadrilateral ABCD if A(3, 0), B(5, 3), C(0, 7) and D(–2, 0).
Answer: 2 √58

Question. Find the value of y if the points A(5, y), B(1, 5), C(2, 1) and D(6, 2) are the vertices of the square.
Answer: 6