Consider the diagram below

Which of the following represents the values of x, y, and z?

I took the same test, its B, I got it right.

For proof, I solved y for 4sqrt2. A says x=y which cant be true, so it has to be B, the only other option with y=4sqrt2 in which x=4sqrt6

(sqrt means square root)

rhombus

Step-by-step explanation:

First we determine if the sides are parallel and if the angles are 90°.  To do this, we find the slope of each side using the formula

For WX, we have

m = (4-1)/(-1-1) = 3/-2

For XY, we have

m = (1--2)/(1--1) = 3/2

For YZ, we have

m = (-2-1)/(-1--3) = -3/2

For ZW, we have

m = (1-4)/(-3--1) = -3/-2 = 3/2

Parallel lines have the same slope; this means that WX and YZ are parallel, as are XY and ZW.

Lines that make a 90° angle are called perpendicular lines, and they have slopes that are negative reciprocals of one another (meaning they have opposite signs and are flipped).  None of these are negative reciprocals; this means none of the angles are 90°.  This tells us this is not a square nor a rectangle.

To determine if this is a rhombus, we use the distance formula to find the length of each side:

The length of WX is

The length of XY is

Since both pairs of opposite sides are parallel, this means opposite sides will be congruent; this tells us all four sides will be congruent, and this is a rhombus.