On the figure below you can click and drag the red figure and its points as well as the point P.[br][br]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'?[br][br]Be sure to drag P and Q around to various locations and use various angle measures![br][br]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 [math]m\angle QPQ'[/math] and the angle of rotation?[br][br]Be sure to drag P and Q around to various locations and use various angle measures![br][br]Would you expect this relationship to be the same for [math]m\angle RPR'[/math] and [math]m\angle SPS'[/math]? Why or why not?
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.[br][br]Click and drag the points on the pre-image and use the slider to change the angle of rotation.[br][br]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°".[br][br]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.[br][br]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.[br][br]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.