Let us look at the images of polygons under rotation.
Click the "On/Off" button on the applet to start it.
Let us start with line segments. Experiment with the applet and try predict where the image of a line segment will be.
If the object is a line segment, what angles of rotation give you a perpendicular line segment?
Where is the center of rotation if a line segment and its image lie on the same line under a rotation of angle 180°?
Draw a square on the applet (use the graph paper lines to make your square accurate). Now change the mode so that a red dot appears in the middle of the square and drag it so that it is at the center of rotation. Now change mode again and find the four angles of rotation make the imgae of the square coincide with the square. We say that the square has rotational symmetry of order four.
Clear the applet and once again draw a square this time with vertices at (-5,0), (0,0), (0,-5), and (-5,-5). Find three different rotations for which the image of this square is a square with vertices (5,5), (10,5), (5,10), (10,10).
e-mail: C. Mawata