Without using Pythagoras theorem, show that `A(4,4),\ B(3,5)a n d\ C(-1,-1)` are the vertices of a right angled triangle.

Explanation

Slope of `AB=frac{y_{2}-y_{1}}{x_{2}-x_{1}}=frac{2-4}{1-0}=-2`

Slope of` B C=frac{y_{2}-y_{1}}{x_{2}-x_{1}}=frac{3-2}{3-1}=frac{1}{2}`

Slope of` A B times Slope of B C=-2 times frac{1}{2}=-1`

therefore Angle between `A B` and` B C=frac{pi}{2}`

therefore `A B C` are the vertices of a right angled triangle.