Question

Quadrilateral WXYZ has vertices W(2, 10), X(10, 10), (10,2), and Z(2, 2). Determine if quadrilateral WXYZ is a rhombus.

A. No, quadrilateral WXYZ is not a rhombus.
B. Yes, quadrilateral WXYZ is rhombus because the sides are perpendicular.
C. Yes, quadrilateral WXYZ is a rhombus because the slopes of the diagonals are perpendicular.
D. There is not enough information to determine.
Please select the best answer from the choices provided

Answer 1

B. Yes, quadrilateral WXYZ is rhombus because the sides are perpendicular.

Explanation:

1) according to the given coordinates the equations of the sides are:

YZ: y=2; WZ: x=2; WX: y=10; XY: x=10. It means

2) YZ⊥WZ; YZ⊥XY; WX⊥XY; WX⊥WZ. To the additional, WX=WZ=YZ=XY, then

3) the given quadrilateral is sqare (rhombus with angles m∠=90°).

4) finally, the correct answer is

B. Yes, quadrilateral WXYZ is rhombus because the sides are perpendicular.