# Chapter 12: Rigid Transformations

**At Grade**Created by: CK-12

## Introduction

The final chapter of Geometry explores transformations. A transformation is a move, flip, or rotation of an image. First, we will look at different types of symmetry and then discuss the different types of transformations. Finally, we will compose transformations and look at tessellations.

## Chapter Outline

- 12.1. Reflection Symmetry
- 12.2. Rotation Symmetry
- 12.3. Geometric Translations
- 12.4. Rotations
- 12.5. Reflections
- 12.6. Composition of Transformations
- 12.7. Tessellations

### Chapter Summary

## Summary

This chapter discusses transformations of figures in the two-dimensional space. It begins with an explanation of reflection and rotation symmetry. The chapter then branches out to discuss the different types of rigid transformations: translation (sliding a figure to a new position), rotation (rotating a figure with respect to an axis), and reflection (flipping a figure along a line of symmetry). Once the different types of basic transformations are discussed, the composition of these actions to create a new type of transformation is explored. The chapter wraps up with a detailed presentation of tessellations.

### Chapter Review

Match the description with its rule.

- Reflection over the \begin{align*}y-\end{align*}axis - A. \begin{align*}(2a - x, y)\end{align*}
- Reflection over the \begin{align*}x-\end{align*}axis - B. \begin{align*}(-y, -x)\end{align*}
- Reflection over \begin{align*}x = a\end{align*} - C. \begin{align*}(-x, y)\end{align*}
- Reflection over \begin{align*}y = b\end{align*} - D. \begin{align*}(-y, x)\end{align*}
- Reflection over \begin{align*}y = x\end{align*} - E. \begin{align*}(x, -y)\end{align*}
- Reflection over \begin{align*}y = -x\end{align*} - F. \begin{align*}(x, 2b - y)\end{align*}
- Rotation of \begin{align*}180^\circ\end{align*} - G. \begin{align*}(x, y)\end{align*}
- Rotation of \begin{align*}90^\circ\end{align*} - H. \begin{align*}(-x, -y)\end{align*}
- Rotation of \begin{align*}270^\circ\end{align*} - I. \begin{align*}(y, -x)\end{align*}
- Rotation of \begin{align*}360^\circ\end{align*} - J. \begin{align*}(y, x)\end{align*}

### Texas Instruments Resources

*In the CK-12 Texas Instruments Geometry FlexBook® resource, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9697.*

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## Date Created:

Aug 09, 2013## Last Modified:

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