Line through square corners

David Taub
The four colored shapes in this image are all squares with their bottom edges on the x-axis. The line goes through their corners. Their edges are aligned as seen. Try and answer the following questions given in terms of A and B.
  1. Find the coordinates of points C and D.
  2. Find the area of the small orange square and the large blue square.
  3. Find the equation of the line through the corners.
  4. Is the percent difference the same between any two adjacent squares?
  5. Imagine a pattern of images of ever larger squares, where the green square is image 1, the red square is image 2 and blue square is image 3. What is the area of the square in image n
If the general problem is too hard, you can start by solving it for A=4 and B=7.