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# Chapter 12: Rigid Transformations

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 $y-$axis
• Reflection over the $x-$axis
• Reflection over $x = a$
• Reflection over $y = b$
• Reflection over $y = x$
• Reflection over $y = -x$
• Rotation
• Center of Rotation
• Rotation of $180^\circ$
• Rotation of $90^\circ$
• Rotation of $270^\circ$
• 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 $y-$axis - A. $(2a - x, y)$
2. Reflection over the $x-$axis - B. $(-y, -x)$
3. Reflection over $x = a$ - C. $(-x, y)$
4. Reflection over $y = b$ - D. $(-y, x)$
5. Reflection over $y = x$ - E. $(x, -y)$
6. Reflection over $y = -x$ - F. $(x, 2b - y)$
7. Rotation of $180^\circ$ - G. $(x, y)$
8. Rotation of $90^\circ$ - H. $(-x, -y)$
9. Rotation of $270^\circ$ - I. $(y, -x)$
10. Rotation of $360^\circ$ - J. $(y, x)$

### 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