Rotations!
Definition of a Rotation
On the figure below you can click and drag the red figure and its points as well as the point P.
Dragging the slider to a value greater 0 will rotate the figure about the point P by the corresponding angle measure.
What do you notice about PQ and PQ'? Be sure to drag P and Q around to various locations and use various angle measures! Would you expect the relationship to the be the same for PR and PR'? What about PS and PS'? Why or why not?
What do you notice about and the angle of rotation? Be sure to drag P and Q around to various locations and use various angle measures! Would you expect this relationship to be the same for and ? Why or why not?
Rotations in the Coordinate Plane
Now you will explore 3 common rotations in the coordinate plane. The rotations will be of 90°, 180°, and 270° and will all be about the origin.
Click and drag the points on the pre-image and use the slider to change the angle of rotation.
On a separate piece of paper, create a chart with 4 columns and at least 6 rows. In the first row, label the columns "Original", "90°", "180°", "270°".
Record the original (red) coordinates in the left most column. Record the image (green) coordinates after a 90° rotation in the second column (make sure A' is in the same row as A!). Repeat this process for 180° and 270° rotations.
In the bottom row, try to determine a general rule for each of the rotations. If you do not notice a pattern with the four points, try dragging A, B, C, and D to create a new polygon and extend your table with the new coordinates for each rotation.
Be sure that your rules work even for "weird" cases, such as when the pre-image polygon is not contained in a single quadrant of the plane.