Question

Find the area of the triangle with the vertices (2,3), (4,1), (5,0).

(a) 3 sq.units

(b) 2 sq.units

(c) 0

(d) 1 sq.unit

I got this question in my homework.

This interesting question is from Area of a Triangle in portion Determinants of Mathematics – Class 12

Answer 1

The correct answer is (c) 0

For explanation: The area of the triangle with vertices (2,3), (4,1), (5,0) is given by

Δ=\(\frac{1}{2}\begin{Vmatrix}2&3&1\\4&1&1\\5&0&1\end{Vmatrix}\)

Applying R2→R2-R3

Δ=\(\frac{1}{2}\begin{Vmatrix}2&3&1\\-1&1&0\\5&0&1\end{Vmatrix}\)

Expanding along R2, we get

Δ=\(\frac{1}{2}\) {-(-1)(3-0)+1(2-5)}

Δ=\(\frac{1}{2}\) (0-0)=0.