Question

What will be the area of a triangle whose vertices are (3, 1), (0, 4) and (5, 9)?

(a) 5 units

(b) -5 units

(c) -15 units

(d) 15 units

I had been asked this question in an interview for internship.

The query is from Geometry in section Coordinate Geometry of Mathematics – Class 10

Answer 1

Correct choice is (c) -15 units

To explain I would say: We know that, area of triangle = \(\frac {1}{2}\){x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2 )}

The coordinates of vertices of the triangle are (3, 1), (0, 4) and (5, 9).

The area of triangle = \(\frac {1}{2}\){3(4 – 9) + 0(9 – 1) + 5(1 – 4) } = \(\frac {1}{2}\) {-15 + 0 – 15} = \(\frac {-30}{2}\) = -15 units

Since area of triangle cannot be zero. So area of triangle is 15 units.