Question

Find area of the triangle whose vertices are:
$(2,3),(-1,0),(2,-4)$

Answer 1

(i) Let $(x_1,y_1)=(2,3)$, $(x_2,y_2)=(-1,0)$ and $(x_3,y_3)=(2,-4)$,
Area of a triangle
$=\frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]$
$\Rightarrow$ Area of the given triangle
= $\frac{1}{2}[2\{0-(-4\left)\right\}+(-1)\left\{\right(-4)-(3\left)\right\}+2(3-0\left)\right]$
$=\frac{1}{2}\{8+7+6\}$
$=\frac{21}{2}$ square units.