Question

Find the area of $\Delta ABC$ whose vertices are $A(-5,7),B(-4,-5)$ and $C(4,5)$.

Answer 1

Area of $\Delta ABC$ whose vertices are is $(x_1,y_1),(x_2,y_2)$ and $(x_3,y_3)$

$=\frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]$

In $\Delta ABC$, vertices are $A(-5,7),B(-4,-5)$ and $C(4,5)$

Area of triangle $=\frac{1}{2}[-5(-5-5)-4(5-7)+4(7+5\left)\right]$

Area of triangle$=$$\frac{10}{2}$

$=5$ sq units.