# Chapter 10: Geometric Transformations

## Introduction

Here you'll learn all about geometric transformations. You will learn about reflections, rotations, translations and dilations. You will also learn the distance formula and the midpoint formulas and see how algebra and geometry are connected.

## Chapter Outline

- 10.1. Translations
- 10.2. Graphs of Translations
- 10.3. Rules for Translations
- 10.4. Reflections
- 10.5. Graphs of Reflections
- 10.6. Rules for Reflections
- 10.7. Rotations
- 10.8. Graphs of Rotations
- 10.9. Rules for Rotations
- 10.10. Dilations
- 10.11. Graphs of Dilations
- 10.12. Rules for Dilations
- 10.13. Composite Transformations
- 10.14. Order of Composite Transformations
- 10.15. Notation for Composite Transformations
- 10.16. The Midpoint Formula
- 10.17. The Distance Formula

### Chapter Summary

## Summary

You learned that there are four geometric transformations. Translations, reflections, and rotations all produce congruent shapes. Congruent shapes are exactly the same shape and size. Translations are slides, reflections are flips, and rotations are turns.

The fourth geometric transformation is the dilation. A dilation produces a shape that is an enlargement or reduction of the preimage.

You also learned that two or more transformations can be performed in sequence. The result is called a composite transformation.

Finally, you learned the midpoint formula and the distance formula. The midpoint of a line segment is the point exactly in the middle of the two endpoints. Sometimes midpoints can help you to find lines of reflection (also known as lines of symmetry). The distance formula helps you to calculate the length of line segments. The distance formula is useful for determining whether or not the corresponding sides of shapes are the same length. This can help you to determine whether one shape has been transformed to create another shape.