Creating Squares
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.