Question

The area of $∆ABO$ with vertices A(a, 0), O(0, 0) and B(0, b) in square units is
(a) ab (b) $\frac{1}{2}ab$ (c) $\frac{1}{2}{a}^2{b}^2$ (d) $\frac{1}{2}{b}^2$

Answer 1

Let A(x₁ = a, y₁ = 0), O(x₂ = 0, y₂ = 0) and B(x₃ = 0, y₃ = b) be the given vertices. So
$$\begin{gathered} \mathrm{Area}\left(∆ABO\right)=\frac{1}{2}\left|x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)\right| \\ =\frac{1}{2}\left|a\left(0-b\right)+0\left(b-0\right)+0\left(0-0\right)\right| \\ =\frac{1}{2}\left|-ab\right|= \\ =\frac{1}{2}ab \end{gathered}$$
Hence, the correct answer is (b).