Rigid Motions: Rotation
On the coordinate grid above I have created an example of a rotation, which is one of the three rigid motions.  In geometry, a rotation is defined as a figure that moves about a fixed point, known as the center of rotation.  This particular transformation requires each vertex to move the same degree and the same direction around the center of rotation.  Each vertex must also be the same distance from the center.  My rotation example displays the pre-image of figure ABCDEF in quadrant one and the image of figure A'B'C'D'E'F' in quadrant three.  It is shown that figure ABCDEF in quadrant one was rotated 180 degrees counter-clockwise and ended up in quadrant three, which is now figure A'B'C'D'E'F'.  If a coordinate plane was not used, the 180 degree counter-clockwise rotation of figure ABCDEF about the origin can be verified as accurate, because each vertex of the pre-image moved the same degree (180) in the same direction (counter-clockwise) around the center of rotation (0,0).  As a result, each vertex is equidistant from the center.  Therefore, this specific rigid motion is proven accurate as it meets each aspect of a rotation.
Rotations Video