Question

Without using the pythagoras theorem, Show that the point $(4,4),(3,5)and(-1,-1)$ are the vertices of a right angled triangle

Answer 1

Let the points be $A(4,4)B(3,5)C(-1,-1)$

slope of side AB is $\frac{5-4}{3-4}=-1$

slope of side AC is $\frac{-1-4}{-1-4}=1$

now product of slopes is $-1$

there fore the $△ABC$ is right triangle