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.

Answer 2

Answer:

I am given that the vertices of quadrilateral PQRS are P(4, 5), Q(6, 6), R(9, 4), and S(7, 2). The slope formula applied to each pair of adjacent vertices gives the slopes of the sides: Since each side has a different slope, none of the sides are parallel. So quadrilateral PQRS is not a parallelogram.

Step-by-step explanation:

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