Exploring and Investigating Rotation Properties

The preimage ABCD has been rotated clockwise -90º around the origin, and the image ABCD was created. What is the center of rotation for the above rotation? Name the point and state its location.

Create line segments from the preimage point to the center of rotation and then to the corresponding image. Measure the distances of these line segments: AE, A'E, BE, B'E, CE, C'E, DE, and D'E. List these distances below and explain what you notice. If you change the image and corresponding preimage, does the relationship you found on the original image and preimage stay the same? If yes, create a property that could describe this relationship.

Measure the angles created from connecting the preimage points to the center of rotation and corresponding image points, i.e. angles DED', CEC', BEB' and AEA.' What did you find? If you change the image and corresponding preimage, does the relationship you found on the original image and preimage stay the same? If yes, explain why this makes sense and create a property to describe the relationship you found.

Regarding location, what do the points on the preimage and the corresponding point on the image have in common? If you change the image and corresponding preimage, does the relationship you found on the original image and preimage stay the same? If yes, create a property that could describe this relationship.

Create a function in two-variables F(x,y)--> ( , ) for the -90º rotation above.

Provide the domain and range of the function for the -90º rotation around the origin.

Compare the preimage and image by measuring the angles of the image and preimage, and by measuring the side lengths. Tell me what you notice. If you change the image and corresponding preimage, does the relationship you found on the original image and preimage stay the same? What property can you write to describe this relationship?

Using the relationships you found above, rotate preimage ABCD 90° counterclockwise and construct the image of this rotation in the graph above. (Hint: you can use the angle with a fixed degree tool to help you find your points). Below, enter the function that describes this rotation.

How would the two variable functions change with each -90º clockwise rotation around the origin (i.e., 90º, -180º, and -270º clockwise rotation)?

How would the two variable function change with each 90º counterclockwise rotation around the origin (i.e. 90º, 180º and 270º counterclockwise rotation)?