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

Let points be `(4,4)=A`, `(3,5)=B` and `(-1,-1)=C`.
`:."Slope of line" AB`,
`(m_(1))=(5-4)/(3-4)=(1)/(-1)=-1`
and slope of line `AC`,
`(m_(2))=(-1-4)/(-1-4)=(-5)/(-5)=1`
`:' m_(1)xxm_(2)=-1xx1=-1`
`:.` Line `AB` is perpendicular to line `AC`.
`:.` In `DeltaABC`, `/_A=90^(@)impliesDeltaABC` is right angled triangle.
Therefore, given points are the vertices of a right angled trigangle.