Question

The area (in sq. units) of the triangle formed by the points $(-3,0),(1,-3)$ and $(4,1)$ is

Answer 1

Let $A=(-3,0),B=(1,-3),C=(4,1)$
Now, $AB=5$
$BC=5AC=5\sqrt{2}$
By observations, we get
$A{B}^2+B{C}^2=A{C}^2$
Therefore, it is a right angled isosceles triangle, so the area is
$Area=\frac{1}{2}\times 5\times 5$
$\Rightarrow Area=12.5$ sq. units