# Line through square corners

- Author:
- David Taub

- Topic:
- Algebra, Area, Straight Lines, Square

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

**and***A**.***B**- Find the coordinates of points C and D.
- Find the area of the small orange square and the large blue square.
- Find the equation of the line through the corners.
- Is the percent difference the same between any two adjacent squares?
- 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

*and***A=4***.***B=7**