Question

3. Quadrilateral ABCD has vertices A (−1, 5), B(4,0), C(1,−5),and D(−5,1). Find the slopes of the sides and then explain whether ABCD is or is not a parallelogram.

Answer 1

Slope of AB=(0-5)/(4-(-1))=-5/5=-1.

Slope of DC=(-5-1)/(1-(-5))=-6/6=-1. So AB and DC are parallel.

Slope of DA=(5-1)/(-1-(-5))=4/4=1. DA is perpendicular to DC and AB.

Slope of CB=(-5-0)/(1-4)=5/3. So DA and CB are not parallel.

The figure is a (right) trapezoid, not a parallelogram.