There are an infinite number of possible solutions. Imagine sliding point X toward A or B. You can aways rotate line XW around X so that W stays on AC. Each angle gives a different solution.
If and only if the points W, X, Y and Z has to be placed on the sides of the rectangle ABCD and Then there is only one unique solution of this question. See attachment #2 to see what happens if is changing but remains constant. Only the thick outlined quadrilateral is a rectangle, all other quadrilaterals are trapezoids.
According to the labeling in attachment #1 you'll get:
........... [1]
The adjacent sides of the rectangle are perpendicular to each other. Using the slopes of the sides you'll get:
........... [2]
From [2] you'll get:
Plug in the term of x into [1] and solve for y. I've to confess that this task was done by my calculator. You'll get:
and consequently
Since you'll get
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