Without using Pythagoras theorem, show that the points `A(2,1)`, `B(5,4)` and `C(3,6)` are the vertices of a right-angled triangle.

Explanation

Slope of line `AB=m_(1)=(4-1)/(5-2)=1`
Slope of `BC=m_(2)=(6-4)/(3-5)=-1`
Here `m_(1)*m_(2)=(1)(-1)=-1`
`implies AB` and `BC` are mutually perpendicular.
`implies DeltaABC` is a right angled triangle.