Question

Prove that $(1,1),(4,4)$ and $(6,2)$ are the vertices of a right angled triangle

Answer 1

From above figure, slopes

$M_{AB}=\frac{4-1}{4-1}=1$

$M_{AC}=\frac{2-1}{6-1}=\frac{1}{5}$

$M_{BC}=\frac{2}{-2}=-1$

$M_{AB}\times M_{BC}=-1$

$\therefore △ABC$ is right angle triangle with $\angle C={90}^o$