CBSE Class 10 Mathematics Coordinate Geometry MCQs

Question : If (a, b) is the mid-point of the line segment joining the points A (10, -6) and B (k, 4) and a - 2b = 18, the value of k is:
(a) 40
(b) 22
(c) 4
(d) 36
Answer : B

Question : Point A (-1, y) and B (5, 7) lie on a circle with centre O (2, -3y). The values of y are:
(a) 1, -7
(b) -2, 7
(c) -2, -7
(d) -1, 7
Answer : D

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 : D

Question : Distance between two points (3, 2) and (6, 6) is:
(a) 5
(b) 3
(c) 2
(d) 8
Answer : A

Question : If the point P (k, 0) divides the line segment joining the points A (2, -2) and B (-7, 4) in the ratio 1:2, then the value of k is :
(a) 1
(b) 2
(c) -1
(d) -2
Answer : C

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

Question : If the point P (6, 2) divides the line segment joining A (6, 5) and B (4, y) in the ratio 3 : 1, then the value of y is :
(a) 4
(b) 2
(c) 1
(d) 3
Answer : C

Question : The line segment joining the points P (-3, 2) and Q (5, 7) is divided by the y- axis in the ratio:
(a) 3 : 1
(b) 3 : 2
(c) 3 : 4
(d) 3 : 5
Answer : D

Question : The distance of the point P (-6, 8) from the origin is:
(a) 14
(b) 6
(c) 8
(d) 10
Answer : D

Question : The mid-point of the line segment joining the points A (-2, 8) and B (-6,-4) is:
(a) (-4, -6)
(b) (-4, 2)
(c) (2, 6)
(d) (6, -2)
Answer : B

Question : The points A(0, –2), B(3, 1), C(0, 4) and D(–3, 1) are the vertices of a
(a) parallelogram
(b) rectangle
(c) square
(d) rhombus

Question : If A(3, 8), B(4, –2) and C(5, –1) are the vertices of ΔABC. Then, its area is
(a) 28(1/2)sq. units
(b) 37(1/2)sq. units
(c) 57sq. units
(d) 75 sq. units

Question : The points A(0, 6), B(–5, 3) and C(3, 1) are the vertices of a triangle which is
(a) isosceles
(b) equilateral
(c) scalene
(d) right angled

Question : Two vertices of ΔABC are A(–1, 4) and B(5, 2) and its centroid is G(0, –3). The coordinate of C is
(a) (4, 3)
(b) (4, 15)
(c) (–4, –15)
(d) (–15, –4)

Question : The coordinates of the centroid of ABC with vertices A(–1, 0), B(5, –2) and C(8, 2) is
(a) (12, 0)
(b) (6, 0)
(c) (0, 6)
(d) (4, 0)

Question : If the points A(2, 3), B(5, k) and C(6, 7) are collinear, then the value of k is
(a) 4
(b) 6
(c) -3 /2 
(d) 11 /4

Question : If P(–1, 1) is the middle point of the line segment joining A(–3, b) and B(1, b + 4) then the value of b is
(a) 1
(b) –1
(c) 2
(d) 0

Question : y–axis divides the join of P(–4, 2) and Q(8, 3) in the ratio
(a) 3 : 1
(b) 1 : 3
(c) 2 : 1
(d) 1 : 2

Question : x–axis divides the join of A(2, –3) and B(5, 6) in the ratio
(a) 3 : 5
(b) 2 : 3
(c) 2 : 1
(d) 1 : 2

Question : The point P(1, 2) divides the join of A(–2, 1) and B(7, 4) are in the ratio of
(a) 3 : 2
(b) 2 : 3
(c) 2 : 1
(d) 1 : 2

Question : A point P divides the join of A(5, –2) and B(9, 6) are in the ratio 3 : 1. The coordinates of P are
(a) (4, 7)
(b) (8, 4)
(c) ( 11/2, 5)
(d) (12, 8)

Question : What point on x – axis is equidistant from the points A(7, 6) and B(–3, 4)?
(a) (0, 4)
(b) (–4, 0)
(c) (3, 0)
(d) (0, 3)

Question : The distance of the point P(4, –3) from the origin is
(a) 1 unit
(b) 7 units
(c) 5 units
(d) 3 units

Question : The distance between the points A(2, –3) and B(2, 2) is
(a) 2 units
(b) 4 units
(c) 5 units
(d) 3 units

Question : Find the area of the triangle whose vertices are A(1, 2), B(–2, 3) and C(–3, –4)
(a) 11sq. units
(b) 22 sq. units
(c) 7 sq. units
(d) 6.5 sq. units

Question : Find the area of the triangle whose vertices are A(2, 4), B(–3, 7) and C(–4, 5)
(a) 11sq. units
(b) 22 sq. units
(c) 7 sq. units
(d) 6.5 sq. units

Question : Find the area of the triangle whose vertices are A(10, –6), B(2, 5) and C(–1, 3)
(a) 12.5 sq. units
(b) 24.5 sq. units
(c) 7 sq. units
(d) 6.5 sq. units

Question : Find the area of the triangle whose vertices are A(4, 4), B(3, –16) and C(3, –2)
(a) 12.5 sq. units
(b) 24.5 sq. units
(c) 7 sq. units
(d) 6.5 sq. units

Question : For what value of x are the points A(–3, 12), B(7, 6) and C(x, 9) collinear?
(a) 1
(b) –1
(c) 2
(d) –2

Question : For what value of y are the points A(1, 4), B(3, y) and C(–3, 16) collinear?
(a) 1
(b) –1
(c) 2
(d) –2

Question : Find the value of p for which the points A(–1, 3), B(2, p) and C(5, –1) collinear?
(a) 1
(b) –1
(c) 2
(d) –2

Question : What is the midpoint of a line with endpoints (–3, 4) and (10, –5)?
(a) (–13, –9)
(b) (–6.5, –4.5)
(c) (3.5, –0.5)
(d) none of these

Question : A straight line is drawn joining the points (3, 4) and (5,6). If the line is extended, the ordinate of the point on the line, whose abscissa is –1 is
(a) 1
(b) –1
(c) 2
(d) 0

Question : If the distance between the points (8, p) and (4, 3) is 5 then value of p is
(a) 6
(b) 0
(c) both (a) and (b)
(d) none of these

Question : The fourth vertex of the rectangle whose three vertices taken in order are (4,1), (7, 4), (13, –2) is
(a) (10, –5)
(b) (10, 5)
(c) (8, 3)
(d) (8, –3)

Question : If four vertices of a parallelogram taken in order are (–3, –1), (a, b), (3, 3) and (4, 3). Then a : b =
(a) 1 : 4
(b) 4 : 1
(c) 1 : 2
(d) 2 : 1

Question : Area of the triangle formed by (1, – 4), (3, – 2) and (– 3,16) is
(a) 40 sq. units
(b) 48 sq. units
(c) 24 sq. units
(d) none of these

Question : The points (2, 5), (4, - 1), (6, - 7) are vertices of an ___________ triangle
(a) isosceles
(b) equilateral
(c) scalene
(d) right angled

Question : The area of triangle formed by the points (p, 2 - 2p), (l-p,2p) and (-4-p, 6- 2p) is 70 sq. units. How many integral value of p are possible ?
(a) 2
(b) 3
(c) 4
(d) none of these

Question : If the origin is the mid-point of the line segment joined by the points (2,3) and (x,y), then the value of (x,y) is
(a) (2, –3)
(b) (2, 3)
(c) (–2, 3)
(d) (–2, –3)

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

Question : The distance between the points A(0, 6) and B(0, -2) is:
(a) 2
(b) 6
(c) 4
(d) 8

Question : The distance of the point P(-6, 8) from the origin is:
(a) 8
(b) 27
(c) 10
(d) 6

Question : The distance between the points (0, 5) and (-5, 0) is:
(a) 5
(b) 52
(c) 25
(d) 10

Question : 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

Question : The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is:
(a) 5
(b) 12
(c) 11
(d) 7 + 5

Question : 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

Question : The points (–4, 0), (4, 0), (0, 3) are the vertices of a :
(a) Right triangle
(b) Isosceles triangle
(c) Equilateral triangle
(d) Scalene triangle

Question : Point on x – axis has coordinates:
(a) (a, 0)
(b) (0, a)
(c) (–a, a)
(d) (a, –a)

Question : Point on y – axis has coordinates:
(a) (–a, b)
(b) (a, 0)
(c) (0, b)
(d) (–a, –b)

Question : Line formed by joining (- 1,1) and (5, 7) is divided by a line x + y = 4 in the ratio of
(a) 1 : 4
(b) 1 : 3
(c) 1 : 2
(d) 3 : 4

Question : If the area of the triangle with vertices (x, 0), (1,1) and (0, 2) is 4 square units, then a value of x is
(a) –2
(b) –4
(c) –6
(d) 8

Question : Point A(–5, 6) is at a distance of:
(a) 61 units from the origin
(b) 11 units from the origin
(c) √61 units from the origin
(d) √11 units from the origin

Question : If the points (1, x), (5, 2) and (9, 5) are collinear then the value of x is
(a) 5/2
(b) -5/2
(c) –1
(d) 1

Question : The end points of diameter of circle are (2, 4) and (–3, –1). The radius of the circle us
(a) 5√2/2
(b) 5√2
(c) 3√2
(d) 15√2/2

Question : The ratio in which x – axis divides the line segment joining the points (5, 4) and (2, –3) is:
(a) 5 : 2
(b) 3 : 4
(c) 2 : 5
(d) 4 : 3

Question : 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

Question : The point which lies on the perpendicular bisector of the line segment joining the points A(–2, – 5) and B(2, 5) is:
(a) (0, 0)
(b) (0, 2)
(c) (2, 0)
(d) (–2, 0)

Question : 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)

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

Question : Three vertices of a parallelogram taken in order are (- 1, - 6), (2, - 5) and (7, 2). The fourth vertex is
(a) (1, 4)
(b) (1, 1)
(c) (4, 4)
(d) (4, 1)

Question : If A and B are the points ( - 3, 4) and (2,1) respectively, then the coordinates of the points on AB produced such that AC = 2BC are
(a) (2, 4)
(b) (3, 7)
(c) (7, –2)
(d) none of these

Question : Distance of the point (4, a) from x-axis is half its distance from y-axis then a =
(a) 2
(b) 8
(c) 4
(d) 6

Question : A triangle is formed by the points 0(0, 0), A(5,0) and B(0,5). The number of points having integral coordinates (both x and y) and strictly inside the triangle is
(a) 10
(b) 17
(c) 16
(d) 6