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

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This presentation is the intellectual property of Christine Markstrum 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.

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This presentation is the intellectual property of Christine Markstrum 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

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

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

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

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

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

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

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This presentation is the intellectual property of Christine Markstrum A B C Examples 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? Name the transformation A’ B’ C’

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

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

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

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

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Translations, Reflections, and Rotations. Vocabulary Transformation- changes the position or orientation of a figure. Image- the resulting figure after.

Translations, Reflections, and Rotations. Vocabulary Transformation- changes the position or orientation of a figure. Image- the resulting figure after.

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