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.