Transformation Project
Due: Nov. 20, 2012, at beginning of class, 3:30 pm to turnitin.com
Assigned: 11/9/12
Due: 11/20/12
Submission: Both a hard copy to instructor and an electronic copy to Turn-It-In.com
Writing Assignment Guidelines
For this assignment you may work with one other student to collaborate and develop your
solutions. Each pair will do their own write up and submit two copies of their paper, one
to Turn-It-In.com, and the other a hard copy to your instructor. All material submitted
should be produced electronically with nothing hand written.
For this project, you are to write your solutions carefully and completely. The
understanding is you will work with one other person, but you may work by yourself.
The purpose of this assignment is to relate the mathematics you have learned to an
application, discover new relationships, to emphasize your writing, and your ability to
explain your mathematical work clearly. Write your paper as if you were writing to a
classmate who knows as much mathematics as you.
Your paper should include the following:
-A good drawing(s) with labels.
-An explanation of your set-up and the work done.
-The actual mathematics involved, paying particular attention to justifying the
mathematics involved.
-Generalizations supported by you work, with good justifications written in complete
sentences.
-The expectation is that your paper will be typed, with all graphs and diagrams produced
electronically.
-Writing style will be a factor in your evaluation. You paper should not read as if you
were just answering some questions in a math class.
Evaluation
This project will be entered into the category of ‘project’ in Power School.
F12
Transformation Project
Due: Nov. 20, 2012, at beginning of class, 3:30 pm to turnitin.com
Assignment: You are to do I and II below, and one of the extensions. You may choose to
do an additional extension for extra credit.
Due Date: Tuesday, Nov. 20, 2012. Hard copies are due to your teacher at the beginning
of class. Also, electronic submissions are due to turnitin.com by 3:30 pm.
Transformations and Matrices
I. Find a matrix that will reflect over the line y  2 x . Give an example of a triangle and
find its image using your matrix. Produce a drawing of both the triangles.
Extension 1: Generalize your solution for any line that passes through the origin, y  mx .
Extension 2: Find a technique for reflecting over the line y  mx  b . Give an example of
a triangle and find its image using your matrix. Produce a drawing of both the triangles.
II. Using matrices, prove that a rotation through an angle  preserves angle measure.
Extension 3: Find a general procedure using matrices for rotation through any point in the
plane. Give an example of a triangle and find its image using your matrix. Produce a
drawing of both the triangles.
8
6
A
4
B
A'
2
C
-10
-5
5
C'
10
B'
-2
-4
-6
-8
F12