The following question is based on Coordinate Geometry:

Show that the points A(3,-1), B(5,-1) and C(3,-3) are the vertices of a right angled isosceles triangle.

Solution:

           AC = √[(3 - 3)^2 + (-3 +1)^2] = 2

           BC = √[(3 - 5)^2 + (-3 +1)^2] = 2√2

           AB = √[(5 - 3)^2 + (-1 +1)^2] = 2

AC = AB

BC2  = AB2 + AC2

Hence they are vertices of a right angled isosceles triangle.