Rotations
A rotation is a transformation in a plane that turns every point of a figure through a specified angle and direction about a fixed point. This applet allows the user to explore the relationship between corresponding vertices when a figure is rotated 90, 180, 270, or 360 degrees counterclockwise about the origin.
Use the checkboxes to toggle on and off figures. Using your mouse, move the points of the blue figure to change the shape of the original figure. Use the slider to change the angle of rotation. As you explore, develop conjectures for the relationship between the coordinates of the vertices of the original figure (blue) and the coordinates of the corresponding vertices of the rotated figure (yellow).
Test your conjectures by toggling on the "Test Your Conjecture" checkbox and one of the "Show [Geometric Figure]" checkboxes. Five red points will appear in the graph. Move the red points to your conjectured coordinates of the vertices of the rotated figure. Once you have moved the red points, toggle on the corresponding "Show Rotated [Geometric Figure]" checkbox. Compare the coordinates of the red points to the coordinates of the vertices of the rotated figure (yellow). Make revisions to your conjectures as necessary.