How to translate the coordinates of a point from pixels into real sizes, if 4 other points are known?

Question

Geometry

Hi all. Not sure if the question accurately reflects the problem.
The bottom line is, I have an image of a room with known pixel coordinates of five points (the image of the room is tilted), there are also the exact dimensions of this room, of which I found the real coordinates of four points. The task is to find the real coordinates of the fifth point.
I drew a picture explaining the essence of the problem visually.

How to calculate manually, or is it really possible to do it only with the help of some script?