Question

What is the area of the triangle whose vertices are (0,1), (0,2), (1,5)?

(a) 1 sq.unit

(b) 2 sq.units

(c) $\frac{1}{3}$ sq.units

(d) $\frac{1}{2}$ sq.units

I got this question in an international level competition.

The question is from Area of a Triangle in chapter Determinants of Mathematics – Class 12

Answer 1

Correct option is (d) $\frac{1}{2}$ sq.units

To elaborate: The area of the triangle with vertices (0,1), (0,2), (1,5) is given by

Δ=$\frac{1}{2}\begin{Vmatrix}0&1&1\\0&2&1\\1&5&1\end{Vmatrix}$

Expanding along C1, we get

Δ=$\frac{1}{2}${(0-0+1(1-2)}=$\frac{1}{2}$ |-1|=$\frac{1}{2}$ sq.units.