CBSE Class 10 Mathematics Coordinate Geometry MCQs Set E

Question. The area of the triangle with vertices (a, b+c), (b, c+a) and (c, a+b) is
(a) a + b + c
(b) a²+b²+c²
(c) 0
(d) (a+b+c)²

Answer: C

Question. The triangle whose vertices are ( – 3, 0), (1, – 3) and (4, 1) is ___________ triangle.
(a) Obtuse triangle
(b) equilateral
(c) right angled isosceles
(d) scalene

Answer: C

Question. The distance of the point (-5, 12) from the y-axis is
(a) 12 units
(b) 5 units
(c) 13 units
(d) -5 units

Answer: B

Question. If two vertices of an equilateral triangle are (3, 0) and (6, 0), the third vertex is
(a) (5/7 , 2√2/ 7)
(b) (3, 9)
(c) (9 /2 , 3 √3/2)
(d) None of the options

Answer: C

Question. If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), the value of p is
(a) √5 units
(b) √8 units
(c) √10 units
(d) None of the options

Answer: C

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

Answer: B

Question. The distance between the points (-8/5,2) and (2/5 ,2) is
(a) 0 units
(b) 1 unit
(c) 2 units
(d) 5 units

Answer: C

Question. (5, –2), (6, 4) and (7, –2) are the vertices of a/an
(a) Scalene triangle
(b) Equilateral triangle
(c) Isosceles triangle
(d) None of the options

Answer: C

Question. The point on the y-axis which is equidistant from (2, –5) and (–2, 9) is
(a) (0, 3)
(b) (0, 2)
(c) (0, 5)
(d) None of the options

Answer: B

Question. The distance between the points (x₁,y₁) and (x²,y²) is given by
(a) √(x₂+x₁)² +(y₂+y₁)² units
(b) √(x₂+x₁)² −(y₂+y₁)² units
(c) √(x₂-x₁)² −(y₂−y₁)² units
(d) √(x₂−x₁)² +(y₂−y₁)² units

Answer: D

Question. Find the value of ‘k’, if the point (0, 2) is equidistant from the points (3, k) and (k, 5)
(a) 2
(b) 0
(c) 1
(d) -1

Answer: C

Question. The distance between the points and is
(a) 0 units
(b) p units
(c) p2 units
(d) 1 units

Answer: B

Question. If the vertices of a triangle are (1, 1), ( – 2, 7) and (3, – 3), then its area is
(a) 0 sq. units
(b) 2 sq. units
(c) 24 sq. units
(d) 12 sq. units

Answer: A

Question. A relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5), is
(a) x + y = 2
(b) x – y = 2
(c) 2x + y = 8
(d) None of the options

Answer: B

Question. Points A(2, –1), B(3, 4), C(–2, 3), D(–3, –2) are the vertices of a:
(a) Rectangle
(b) Square
(c) Rhombus
(d) None of the options

Answer: C

Question. If the distance of P(x, y) from A(5, 1) and B(–1, 5) are equal, then 3x equals
(a) y
(b) y/ 2
(c) 2y
(d) 2/ y

Answer: C

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

Answer: B

Question. The point where the perpendicular bisector of the line segment joining the points A(2, 5) and B(4, 7) cuts is:
(a) (3, 6)
(b) (0, 0)
(c) (2, 5)
(d) (6, 3)

Answer: A

Question. The point ( – 3, 5) lies in the ___________ quadrant
(a) IV
(b) II
(c) III
(d) I

Answer: B

Question. If the distance of P(x, y) from the points A(3, 6) and B(–3, 4) are equal, then 3x + y =
(a) 4
(b) 5
(c) 8
(d) 12

Answer: B

Question. Point A lies on the line segment PQ joining P(6, –6) and Q(–4, –1) in such a way that PA/ PQ = 2/ 5 . If point P also lies on the line 3x + k(y + 1) = 0, the value of k is
(a) k = 12/ 5
(b) k = 9 /5
(c) k = 18/5
(d) k = 0

Answer: C

Question. The ratio in which the line 2x + y – 4 = 0 divides the line segment joining the points A (2, –2) and B (3, 7) is
(a) 3 : 5
(b) 2 : 9
(c) 5 : 7
(d) 4 : 5

Answer: B

Question. Let P and Q be the points of trisection of the line segment joining the points A (2, – 2) and B (–7, 4) such that P is nearer to A. The coordinates of P and Q respectively are
(a) (3, 2), (1, 9)
(b) (–4, 3), (5, 0)
(c) (–3, 7), (2, 7)
(d) (–1, 0), (–4, 2)

Answer: D

Question. The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
(a) 15 units
(b) 10 units
(c) 9 units
(d) 12 units

Answer: D

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) 2√34 units
(b) 3 units
(c) √34 units
(d) 4 units

Answer: C

Question. Points A(3, 1), B(5, 1), C(a, b) and D(4, 3) are vertices of a parallelogram ABCD. The values of a and b are respectively
(a) a = 6, b = 3
(b) a = 2, b = 1
(c) a = 4, b = 2
(d) None of the options

Answer: A

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 A(–2, 5), B(1, –3) and C(a, b) form an isosceles triangle with CB = CA, then 6a – 16b + 19 equals
(a) 0
(b) 2
(c) 5
(d) 9

Answer: A

Question. The distance of the point P (–3, –4) from the x-axis (in units) is
(a) 3 1
(b) –3
(c) 4
(d) 5

Answer: C

Question. The distance between (√2 + 1, 2) and (1, 2 − √2) is
(a) 2
(b) 3
(c) 11
(d) 17

Answer: A

Question. The value of k for which the point (0, 2) is equidistant from two points (3, k) and (k, 5) is
(a) 1
(b) 2
(c) 5
(d) 9

Answer: A

Question. The perpendicular distance of A(5, 12) from the y-axis is
(a) 4
(b) 5
(c) 7
(d) 8

Answer: B

One Word Questions 

Question. (0, 2) and (0, –5) are the co-ordinate of two points lying on _________ axis.
Answer: y

Question. The base BC of an equilateral triangle ABC with side 10cm lies along x=axis such that the mid-point of the base is at the origin. Find the coordinates of point B.
Answer: (–5, 0)

Question. What is the x – coordinate of the point which divides the line joining (1, 2) and (2, 3) in the ratio 4 : 3?
Answer: 11/7

Question. Find the coordinates of points which divides line joining (–4, 0) and (0, 6) in the ratio 1 : 3.
Answer: (–3, 1.5)

Question. Find the ratio in which the line segement joining (–2, –3) and (5, 6) is divided by x-axis.
Answer: 1 : 2

Question. Find the distance of a point P(x, y) from the origin (0, 0).
Answer: √x2 y2

Question. A(3, 2) and B(–2, 1) are two vertices of a ΔABC whose centroid G has coordinates (5/3 , -1/3) . 35 Maths–X (E)
Answer: (4, –4)

Question. Find the ratio in which the line-segements joining the points (6, 4) and (1, –7) is divided internally by the axis of x.
Answer: 4/7

Question. Find the coordinates of a point, which is at a distance of 13 units from the origin and lies on x-axis.
Answer: (13, 0) or (–13, 0)

Question. Find the value of k if the distance between (k, 5) and (4, 5) is 5.
Answer: 9 or (–1)

Question. Find the coordinates of points dividing the points (3, 5) and (7, 9) in the ratio 2 : 3.
Answer: (23/5 , 33/5)

Question. Find the centroid of a triangle whose vertices are (–2, –3), (–1, 0) and (7, –6)
Answer: (4/3 , -3)

Question. What are the coordinate of centroid of trinangle formed by the points (–7, 6), (8, 5), (2, –2)?
Answer: (1, 3)

Question. The points (0, –1), (2, 1), (0, 3) and (–2, 1) are the corners of a square. Find the length of its side.
Answer: √8