Question

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

X(6, 1.5), Y6, -4.5), and Z(-1.5, -4.5). Is
WXYZ a rectangle? Justify your answer.

Answer 1

Explanation:

Given the vertices of the polygon WXYZ, you can plot the coordinates on a graph tool to view if it is a rectangle. The attached plot shows a sketch of a rectangle.However, you can further prove.You know in a rectangle, the length on one side equals that on the other side, which is the same with the width.

So, in polygon WXYZ, you should show that length of side WX=ZY and the width WZ=XY or show that width WZ=XY

W(-1.5,1.5) and X(6,1.5) finding the length of this side;

d=√ (x₂-x₁)²+(y₂-y₁)²

d=√(6--1.5)² + (1.5-1.5)²

d=√ 7.5²

d=7.5

Side WX should be equal to side ZY, hence finding side ZY

Z(-1.5,-4.5) and Y(6,-4.5)

d=√ (6--1.5)² + (-4.5--4.5)²

d=√ 7.5²

d=7.5

This justifies your answer that polygon WXYZ is a rectangle.