Practice Transformation Questions (and some answers and explanations)

Here is a general study guide from 2002

• What kind of isometry is the product? vs Compute or construct the product explicitly given explicit X and Y.

What does "orientation preserving or reversing" mean?

• Here is the multiplication table for orientation

What does "defining data" mean?

To tell precisely what an isometry is, you will need to specify

• Here is a thorough reference on how to answer such questions
• Here is one referece for defining data.

How do I multiply rotations?

• Here is a visualization approach.
• Here is an answer sheet for a quiz.
• Here is another answer for a long problem about "wallpaper" patterns

• A sheet on solving transformation equations algebraically

Double Line Reflections

• Double Line Reflections and Translations

About Triple Line Reflection and Glide Reflections

• Half a Dozen Ways to Understand the Product of a Halfturn and a Line Reflection (lots of pictures)
• More Halfturn and Mirror Symmetry (also lots of pictures)
• Here are definitions and methods for analyzing the product of 3 non-collinear line reflections.
• NEW Three Ways to Analyze the Product of a 90-degree rotation and a line reflection

About the Patterns of Centers in Wallpaper Patterns (Crystallography)

• An Explanation of all the Patterns (look for the 4-fold rotations)
• Escher Links
• Lab 9
  • Lab 9 patterns illustrated.
  • Questions about patterns from Lab 9
  • Glide Reflections in the last pattern in Lab 9

Transforming Objects and Figures

• Angles Between a Line and its Rotated Image

Old Final Exams

Check out the transformation problems. Some problems (e.g., affine and barycentric coordinates) you should ignore, since you have not seen those topics yet.

• Final Exam 2001 (pdf) -- Study links from 2001
• Final Exam 2002
• Final Exam 2003
• Final Exam 2004