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.
According to the labeling in attachment #1 you'll get:
The adjacent sides of the rectangle are perpendicular to each other. Using the slopes of the sides you'll get:
From  you'll get:
Plug in the term of x into  and solve for y. I've to confess that this task was done by my calculator. You'll get:
Since you'll get