Composition of Quarter Turns

Composing two different counterclockwise quarter turns (quarter turn around C followed by quarter turn around D) creates a half turn transformation. In this worksheet you can control the positions of the two centers of quarter turn transformations as well as the point being transformed. You can see the specifics of the mappings using the checkboxes on the bottom right.
Challenge yourself by putting a Target point somewhere on the screen using the checkbox on the upper right and moving C, D, and P around so that the image P'' lands on Target.