Answer:
See explanation
Step-by-step explanation:
Polygon WXYZ has vertices W(-1.5, 1.5), X(6, 1.5), Y(6, -4.5), and Z(-1.5, -4.5).
Find the slopes of all sides:
[tex]WX:\ \dfrac{1.5-1.5}{6-(-1.5)}=\dfrac{0}{7.5}=0[/tex] - horizontal line
[tex]XY:\ \dfrac{-4.5-1.5}{6-6}=\dfrac{-6}{0}[/tex] - slope undefined, so the line is vertical
[tex]YZ:\ \dfrac{-4.5-(-4.5)}{-1.5-6}=\dfrac{0}{-7.5}=0[/tex] - horizontal line
[tex]ZW:\ \dfrac{1.5-(-4.5)}{-1.5-(-1.5)}=\dfrac{6}{0}[/tex] - slope undefined, so the line is vertical
Vertical and horizontal lines are perpendicular, so all angles W, X, Y and Z are right angles. Hence, quadrilateral WXYZ is a rectangle
