Shape 

Copyright David & Cynthia Thomas, 2009

Linear Transformations--Exercises

Part I

Do the directed activities in this section.

Part II

Complete the following exercises

1. Identify the following transformation and draw in the appropriate slide arrows, mirrors, turn centers, turn angles, and/or dilation centers.

a.	b.
c.	d.

2. Find the images of the following objects under the indicated transformations.

Translate given slide arrow a

Rotate  about point P by

3. Investigate whether, in general, composition of transformations is commutative.  For instance, given a translation T and a rotation R and compositions T*R (first rotate, then translate) and R*T (first translate, then rotate), is it always true that T*R = R*T?  Illustrate and explain your response using the Geometers Sketchpad.  

4. Image 1 is an old photograph of the author, David Thomas.  Image 2 and Image 3 were created by transforming Image 1. 

a. Discuss the geometric transformations used to create Image 2 and Image 3.

b. Why are Image 2 and Image 3 so different? 

Image 1                     Image 2                      Image 3