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GeoGebraGeoGebra Classroom

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.