Question

10. Polygon WXYZ has vertices W(-1.5, 1.5),

X(6, 1.5), Y(6, -4.5), and Z(-1.5, -4.5). Is
WXYZ a rectangle? Justify your answer.

Answer 1

See explanation

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:

`WX:\ (1.5-1.5)/(6-(-1.5))=(0)/(7.5)=0` - horizontal line

`XY:\ (-4.5-1.5)/(6-6)=(-6)/(0)` - slope undefined, so the line is vertical

`YZ:\ (-4.5-(-4.5))/(-1.5-6)=(0)/(-7.5)=0` - horizontal line

`ZW:\ (1.5-(-4.5))/(-1.5-(-1.5))=(6)/(0)` - 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