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Chapter 7 Transformations

Chapter 7 Transformations. 7.1 Rigid Motion in a Plane. California Standards for Geometry 17: Prove theorems using coordinate geometry 22: Know the effect of rigid motions on figures in the coordinate plane. Definitions. Transformation

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Chapter 7 Transformations

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  1. Chapter 7Transformations This presentation is the intellectual property of Christine Markstrum

  2. 7.1 Rigid Motion in a Plane California Standards for Geometry 17: Prove theorems using coordinate geometry 22: Know the effect of rigid motions on figures in the coordinate plane. This presentation is the intellectual property of Christine Markstrum

  3. Definitions • Transformation • Creating a copy of a figure on the coordinate plane. • The copy is called the IMAGE. • The original figure is called the PREIMAGE. • Three basic transformations • Translation • Reflection in a line • Rotation about a point This presentation is the intellectual property of Christine Markstrum

  4. preimage image Definitions • Translation • The image slides away from the preimage along a line. This presentation is the intellectual property of Christine Markstrum

  5. image preimage Definitions • Reflection • The image is mirrored across a line from the preimage This presentation is the intellectual property of Christine Markstrum

  6. image preimage Defintions • Rotation • The image is turned about a point from the preimage This presentation is the intellectual property of Christine Markstrum

  7. Definitions • An image is named as the “preimage prime” This is hexagon “ABCDEF prime” C D B E C’ D’ B’ F E’ A This is hexagon ABCDEF F’ A’ When you see an ’ in math say “prime” This presentation is the intellectual property of Christine Markstrum

  8. A B C’ C B’ A’ Examples Name the transformation • Translation? • did the image slide away from the preimage? • Reflection? • Rotation? This presentation is the intellectual property of Christine Markstrum

  9. A B C’ C B’ A’ Examples Name the transformation • Translation? • did the image slide away from the preimage? • Reflection? • is the image mirrored across a line from the preimage? • Rotation? This presentation is the intellectual property of Christine Markstrum

  10. A B C’ C B’ A’ Examples Name the transformation • Translation? • did the image slide away from the preimage? • Reflection? • is the image mirrored across a line from the preimage? • Rotation? • is the image turned about a point from the preimage? This presentation is the intellectual property of Christine Markstrum

  11. A B C’ C B’ A’ Examples Describe the transformation Rotation The image appears to rotate around ____________ The angle of rotation is ______ (0, 0) 180o The transformation is a 180o rotation about (0, 0) This presentation is the intellectual property of Christine Markstrum

  12. Definitions • Isometry • A transformation that maintains lengths. • The image and preimage are congruent • Angle measures, parallel lines, and distances between points are also maintained. This presentation is the intellectual property of Christine Markstrum

  13. is a rotation 4 in K L 5 in 25o J 80o M 7 in P N 8 in O Q U 95o 6 in S 5 in R T This presentation is the intellectual property of Christine Markstrum

  14. Summary • What is a transformation? • Describe the three basic transformations. • What is an isometry? Remember to use your own words. This presentation is the intellectual property of Christine Markstrum

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