Question

WXZY is a quadrilateral with W located at (-5, 2) and X is located at (3, 0). What must be the slope of ZY in order for WXYZ to be a parallelogram?

Answer 1

Answer:  The answer is $-\dfrac{1}{4}.$

Step-by-step explanation:  Given that WXZY is a quadrilateral with W located at (-5, 2) and X is located at (3, 0). We need to find the slope of ZY for which the quadrilateral WXZY is a parallelogram.

We know that the opposite sides of a parallelogram are parallel to each other. So, in the attached figure, we must have WX parallel to ZY. And for that, slope of WX = slope of ZY.

Slope of WX is given by

$m=\dfrac{0-2}{3-(-5)}=\dfrac{-2}{8}=-\dfrac{1}{4}.$

Thus, the slope of ZY must be $-\dfrac{1}{2}.$