Question

The vertices of quadrilateral PQRS are P(4, 5), Q(6, 6), R(9, 4), and S(7, 2). Write a paragraph proof to determine whether quadrilateral PQRS is a parallelogram.

Answer 1

The vector PQ is Q-P = (2, 1). The vector SR is R-S = (2, 2). One is not a multiple of the others, so the vectors are not parallel. In a parallelogram, these vectors would be identical. PQRS is not a parallelogram.