Question

Prove that the points $A(-5,4);B(-1,-2)$ and $C(5,2)$ are the vertices of an isosceles right angled triangle.

Answer 1

$A(-5,4)$ , $B(-1,-2)$ and $C(5,2)$

using distance formula for finding distance between two points .

$AB=\sqrt{(-5+1)²+(4+2)²}=\sqrt{(}4²+6²)=2\sqrt{1}3$

$BC=\sqrt{(-1-5)²+(-2-2)²}=\sqrt{(}6²+4²)=2\sqrt{1}3$

$CA=\sqrt{5+5)²+(2-4)²}=\sqrt{(}10²+2²)=2\sqrt{2}6$

hence we can see that it is Right isosceles triangle.