<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
You are reading an older version of this FlexBook® textbook: CK-12 Geometry Concepts Go to the latest version.

# Chapter 12: Rigid Transformations

Difficulty Level: 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.

## 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 Keywords

• Line of Symmetry
• Line Symmetry
• Rotational Symmetry
• Center of Rotation
• angle of rotation
• Transformation
• Rigid Transformation
• Translation
• Vector
• Reflection
• Line of Reflection
• Reflection over the y\begin{align*}y-\end{align*}axis
• Reflection over the x\begin{align*}x-\end{align*}axis
• Reflection over x=a\begin{align*}x = a\end{align*}
• Reflection over y=b\begin{align*}y = b\end{align*}
• Reflection over y=x\begin{align*}y = x\end{align*}
• Reflection over y=x\begin{align*}y = -x\end{align*}
• Rotation
• Center of Rotation
• Rotation of 180\begin{align*}180^\circ\end{align*}
• Rotation of 90\begin{align*}90^\circ\end{align*}
• Rotation of 270\begin{align*}270^\circ\end{align*}
• Composition (of transformations)
• Glide Reflection
• Reflections over Parallel Lines Theorem
• Reflection over the Axes Theorem
• Reflection over Intersecting Lines Theorem
• Tessellation

### Chapter Review

Match the description with its rule.

1. Reflection over the y\begin{align*}y-\end{align*}axis - A. (2ax,y)\begin{align*}(2a - x, y)\end{align*}
2. Reflection over the x\begin{align*}x-\end{align*}axis - B. (y,x)\begin{align*}(-y, -x)\end{align*}
3. Reflection over x=a\begin{align*}x = a\end{align*} - C. (x,y)\begin{align*}(-x, y)\end{align*}
4. Reflection over y=b\begin{align*}y = b\end{align*} - D. (y,x)\begin{align*}(-y, x)\end{align*}
5. Reflection over y=x\begin{align*}y = x\end{align*} - E. (x,y)\begin{align*}(x, -y)\end{align*}
6. Reflection over y=x\begin{align*}y = -x\end{align*} - F. (x,2by)\begin{align*}(x, 2b - y)\end{align*}
7. Rotation of 180\begin{align*}180^\circ\end{align*} - G. (x,y)\begin{align*}(x, y)\end{align*}
8. Rotation of 90\begin{align*}90^\circ\end{align*} - H. (x,y)\begin{align*}(-x, -y)\end{align*}
9. Rotation of 270\begin{align*}270^\circ\end{align*} - I. (y,x)\begin{align*}(y, -x)\end{align*}
10. Rotation of 360\begin{align*}360^\circ\end{align*} - J. (y,x)\begin{align*}(y, x)\end{align*}

### Texas Instruments Resources

In the CK-12 Texas Instruments Geometry FlexBook, 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.

Jul 17, 2012