Question

Prove that the points A(1,0),B(5,3),C(2,7),D(-2,4) are the vertices of a parallelogram

Answer 1

Distance between AB=√(5-1)^2+3^2

=√16+9=5

Distance between BC=√(2-5)^2+(7-3)^2 =5

Distance between CD=√(-2-2)^2+(4-7)^2=5

Distance between DA=√(-2-1)^2+4-0^2=5

Distance between AC=√(2-1)^2+7^2=√50

Distance between BD=√(-2-5)^2+(4-3)^2=√50.

So,it forms a square.A square is also a parallelogram.