Question

What is the area of the triangle if the vertices are (0,2), (0, 0), (3, 0)?

(a) 1 sq.unit

(b) 5 sq.units

(c) 2 sq.units

(d) 3 sq.units

I have been asked this question in exam.

I would like to ask this question from Area of a Triangle in section Determinants of Mathematics – Class 12

Answer 1

The correct answer is (d) 3 sq.units

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

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

Expanding along R3, we get

Δ=\(\frac{1}{2}\) {0-0+3(2-0)}

Δ=3 sq.units.