Rotations and Rotational Symmetry

by

Michelle Brantley

Objective: To understand the effects of rotation on geometric figures. To be able to make conjectures regarding geometric effects as well as algebraic effects.

Materials: GSP

Time: 1-2 days

Level of Difficulty: Medium

Procedure:

1. Construct a triangle in the 1st quadrant . Label those coordinates by highlighting each vertex and clicking on Measure. Click on Coordinates.

2. Now we are ready to rotate the given triangle around the origin 90 degrees. Click on the origin. Under the Transform Menu, click on Mark center "A". Select the entire object and click on Rotate. Rotate the triangle 90 degrees.

In which quadrant is the translated triangle located? How could you rotate the triangle in to the 3rd quadrant? the 4th quadrant?

3. How would the rotations change if the angle of rotation was divided by 2? How many 45 degree rotations would it take for the figure to return to the original position in the 1st quadrant?

4. How would you change the angle of rotation to rotate in the other direction?

5. Now we want to investigate the relationship between the coordinates of the original figure compared to its image. For each rotation, (45 degree clockwise, 45 degree counterclockwise, 90 degree clockwise and 90 degree counterclockwise) find any potential relationships between the original figure's coordinates and the image's coordinates.