### 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)

Related: Maths Trigonometry Sample Questions

**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

a^{3} + b^{3} + c^{3} =

(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)