Question

What will be the area of triangle formed by joining the points P (2, 3), Q (4, 6) and R (6, 9)?

(a) 0

(b) 2

(c) 3

(d) 4

The question was asked in an online interview.

My doubt stems from Geometry topic in division Coordinate Geometry of Mathematics – Class 10

Answer 1

Correct choice is (a) 0

Easy explanation: We know that, area of triangle = \(\frac {1}{2}\){x1 (y2 – y3 ) + x2 (y3 – y1 ) + x3 (y1 – y2 )}

Let us assume the vertices of the triangle are (2, 3), (4, 6) and (6, 9).

The area of triangle = \(\frac {1}{2}\) {2(6 – 9) + 4(9 – 3) + 6(3 – 6) } = \(\frac {1}{2}\){0} = 0 units

Hence, the area of triangle is zero, the points are collinear.