Parallelogram abcd has vertices: a(-3,1), b(3, 3), c(4,0), and d(-2,-2). in two or more complete sentences, explain how you can use the coordinates of the vertices to prove that parallelogram abcd is a rectangle.

A rectangle is a quadrilateral and also a parallelogram whose angles are all right angles. We also know that the two diagonals of any rectangle have the same length. Hence, to prove that parallelogram ABCD is a rectangle we just need to verify that the diagonals have the same length. To do so, let's use the distance formula:

DISTANCE FROM A TO C:

DISTANCE FROM B TO D:

As you can see:

then the parallelogram is definitively a rectangle