[b]Rotation Exploration[/b][br][br]Use the applet below to explore the properties of rotating a polygon around different points on the coordinate plane.

1. If you rotate the polygon 90 degrees around point I (the origin), what are the new coordinates for the vertices? How do these compare to the original coordinates?[br][br]If you rotate the polygon 180 degrees around the origin, what are the new coordinates for the vertices? How do these compare to the original coordinates?[br][br]Consider the point (5, 1). If you rotate this point 90 degrees counter-clockwise around the origin, how would the x and y coordinates change? Is the rotated point closer to the origin, further from the origin, or the same distance?[br][br]2. If you rotate the polygon 90 degrees around point H, what are the new coordinates for the vertices? How do these compare to the original coordinates?[br][br]If you rotate the polygon 180 degrees around point H, what are the new coordinates for the vertices? How do these compare to the original coordinates?[br][br]How is rotating around point H different from rotating around the origin?[br][br]3. If you rotate the polygon 90 degrees around point J, what are the new coordinates for the vertices? How do these compare to the original coordinates?[br][br]4. Predict what the coordinates of the polygon will be if you rotate it 90 degrees around point K. Check your predictions. Were you correct? If not, why were your predictions off?