# Creating Squares

- Author:
- Tim Brzezinski

- Topic:
- Algebra, Geometry, Parallelogram, Quadrilaterals, Rectangle, Rhombus, Square

Creation of this problem was inspired by an Open Middle problem submitted by John Mahlstedt. Even though this problem is different from his submitted problem, they both share a common theme.

## DIRECTIONS:

Move

**the vertices**of the quadrilateral below so that the following conditions are met: 1) No 2 coordinates have the same absolute value. 2) The absolute values of all coordinates are integers ranging from 0 to 9. 3) The quadrilateral formed is a square. Once you form a quadrilateral that meets all these conditions, you'll see a**SQUARE!**sign appear. How many different setups can you create?Suppose the applet above didn't indicate to you that your quadrilateral was a square. How could you prove this using coordinate geometry? Do so below.

Suppose the applet above didn't indicate to you that your quadrilateral was a square. How could you prove this using coordinate geometry? Do so below.