quadrilateral abcd has vertices at A(-2,1) B(7,7) C(3,-1) and D (-6,-7)

Answer 1

Hello,

By definition, a quadrilateral is a parallelogram if both pairs of opposite sides are parallel. So in this case, we need to prove that AB is parallel to CD and that BC is parallel to AD.

Parallel lines have equivalent slopes, so we need the slopes of AB and CD to be equivalent, and the slopes of BC and AD to be equivalent. We can find the slopes using the coordinates.

Slope of AB = (y_B-y_A)/(x_B-x_A) = (7-1)/(7--2) = 6/9 = 2/3

Slope of CD = (y_D-y_C)/(x_D-x_C) = (-7--1)/(-6-3) = -6/-9 = 2/3

Slope of AB = Slope of CD, therefore AB || CD

Do the same for BC and AD and you should have everything you need!