How to reverse a rotated rectangle?

Question

Say there's a rectangle at (20, 20)(fig. 1), then it's rotated 45 degree (fig. 2), if I just have the rotated rectangle and know it's size and rotated degree, is there a way to reverse the rotation and get the original starting point (20, 20)?

fig. 1 fig. 2

Answer 1

Hint

Let point $A$ denote (14,105) and let point $B$ denote (120,70)

You know the angle that $\overline{AB}$ makes with the horizontal. Therefore, you should be able to add $45^{\circ}$ to that to get the new angle that $\overline{AB}$ makes with the horizontal.

Now you have a ray, emanating from point $B$. Also, you know the distance of $\overline{AB}$. Therefore, you know how far to traverse along the ray to identify the original point $A$.