Question

The area of a triangle with vertices at (−4, −1), (1, 2) and (4, −3) is
(a) 17
(b) 16
(c) 15
(d) none of these

Answer 1

(a) 17
Let A be the area of the triangle formed by the points (−4, −1), (1, 2) and (4, −3).

$$\begin{gathered} \therefore A=\frac{1}{2}\left|\left\{x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)\right\}\right| \\ \Rightarrow A=\frac{1}{2}\left|\left\{-4\left(2+3\right)+1\left(-3+1\right)+4\left(-1-2\right)\right\}\right| \\ \Rightarrow A=17 \end{gathered}$$