Quadrilateral PQRS has vertices P(8,0), Q(6,4), R(-2,0), and S(0,-4). Prove that PQRS is a rectangle.

Answer 1

Draw a figure!

You need to prove that length of PQ = length of RS and length of QR = length of PS.

Use the distance formula to do that.

Then compute the diagonals using the theorem of Pythagoras and show that they are equal.

Once you know that it is simple geometry to show that the angles are all right angles.