Question

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

Answer 1

Let the given points be $A(-2,3),B(8,3),C(6,7)$

Now, the $ar\left(\Delta ABC\right)=\frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]$

$=\frac{1}{2}[-2(3-7)+8(7-3)+6(3-3\left)\right]$

$=\frac{1}{2}[-2(-4)+8(4)+6(0\left)\right]$

$=\frac{1}{2}[8+32+0]$

$=\frac{1}{2}\times 40$

$=20$ sq.units

$ar\left(\Delta ABC\right)=20$ sq.units