# Coordinate Geometry Questions and Answers

### Important Questions for Coordinate Geometry (Mathematics):

Ques. If x is a positive integer such that the distance between points P(x, 2) and Q(3, –6) is 10 units, then x is equal to
(a) 3
(b) –3
(c) 9
(d) –9
Ans. (c)

Ques. A line segment is of length 10 units. If the coordinates of its one end are (2, –3) and the abscissa of the other end is 10, then its ordinate is
(a) 9, 6
(b) 3, -9
(c) –3, 9
(d) 9, -6
Ans. (b)

Related: Time and Work question

Ques. If the points (k, 2k), (3k, 3k) and (3, 1) are collinear, then k
(a) 1/3
(b) –1/3
(c) 2/3
(d) –2/3
Ans. (b)

Ques. The coordinates of the point on X-axis which are equidistant from the points (-3, 4) and (2, 5) are
(a) (20, 0)
(b) (-23, 0)
(c) (4/5, 0)
(d) none of these
Ans. (d)

Ques. If (–1, 2), (2, –1) and (3, 1) are any three vertices of a parallelogram, then
(a) a = 2, b = 0
(b) a = –2, b = 0
(c) a = –2, b = 6
(d) a = 6, b = 2
Ans. (c)

Related: Equation of a Straight line MCQs

Ques. The area of the triangle formed by (a, b + c), (b, c + a) and (c, a + b) is
(a) a + b + c
(b) abc
(c) (a + b + c)2
(d) 0
Ans. (d)

Ques. If (x, 2), (-3, -4) and (7, -5) are collinear, then x =
(a) 60
(b) 63
(c) –63
(d) –60
Ans. (c)

Ques. If points (t, 2t), (–2, 6) and (3, 1) are collinear, then t =
(a) ¾
(b) 4/3
(c) 5/3
(d) 3/5
Ans. (b)

Related: Mathematics Complex Numbers

Ques. If the area of the triangle formed by the points (x, 2x), (–2, 6) and (3, 1) is 5 square units, then x =
(a) 2/3
(b) 3/5
(c) 3
(d) 5
Ans. (a)

Ques. If the centroid of a triangle  is (1, 4) and two of its vertices are (4, –3) and (–9, 7), then the area of the triangle is
(a) 183 sq. units
(b) 183/2 sq. units
(c) 366 sq. units
(d) 183/4 sq. units
Ans. (b)

Ques. The line segment joining points (–3, –4), and (1, –2) is divided by y-axis in the ratio
(a) 1 : 3
(b) 2 : 3
(c) 3 : 1
(d) 2 : 3
Ans. (c)

Ques. The ratio in which (4, 5) divides the join of (2, 3) and (7, 8) is
(a) –2 : 3
(b) –3, 2
(c) 3 : 2
(d) 2 : 3
Ans. (d)

Ques. The ratio in which the x-axis divides the segment joining (3, 6) and (12, -3) is
(a) 2 : 1
(b) 1 : 2
(c) –2 : 1
(d)  1 : –2
Ans. (a)

Ques. If the centroid of the triangle formed by the points (a, b) (b, c) and (c, a) is at the origin, then
a3 + b3 + c3 =
(a) abc
(b) 0
(c) a + b + c
(d) 3 abc
Ans. (d)

Related: General Arithmetic Questions

Ques. If the points (1, 2), (–5, 6) and (a, –2) are collinear, then a =
(a) –3
(b) 7
(c) 2
(d) –2
Ans. (b)

Ques. If the centroid of the triangle formed by (7, x), (y, –6) and (9, 10) is at (6, 3), then (x, y) =
(a) (4, 5)
(b) (5, 4)
(c) (–5, –2)
(d) (5, 2)
Ans. (d)