Question

Without using the distance formula, show that the points $A(4,-2),B(-4,4)$ and $C(10,6)$ are the vertices of a right-angled triangle.

Answer 1

Slope of AB $\frac{4+2}{-4-4}=\frac{6}{-8}=\frac{-3}{4}$

Slope of AC $\frac{6+2}{(10-4)}=\frac{8}{6}=\frac{4}{3}$

slope of AB x slope of AC =$\frac{-3}{4}\times \frac{4}{3}=-1$

Hence, it is Right angle triangle.