Section 12-1 Transformations - Reflection SPI 32D: determine whether the plane figure has been reflected given a diagram and vice versa Objectives: Identify.

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Section 12-1 Transformations - Reflection SPI 32D: determine whether the plane figure has been reflected given a diagram and vice versa Objectives: Identify isometries Find reflection images of figures Unit Overview Investigate Transformations  Reflections (this lesson)  Translations  Rotations  Composition of Transformations

Transformation is a change in the original figure (preimage): Preimage Position ShapeSize

Some Basic Transformations Figure Flips PreimageImage Figure Slides PreimageImage Figure Turns Preimage Image

Identifying Isometries Transformation in which the preimage and image are . Isometry NOT Isometry (not congruent)

Transformation Symbols and Notation Transformation maps a figure onto its image. preimage mapping is shown with an arrow. (  ) corresponding image points are shown with a prime symbol (‘) image Write transformation as

In the diagram, XYZ is an image of ABC. b. List all pairs of corresponding sides. a. Name the images of B and C. Naming Images and Corresponding Parts  Y is the image of  B  Z is the image of  C AB and XY, BC and YZ, AC and XZ

Finding Reflection (Flip) Images Isometry in which figure and its image have opposite orientation. Line a is the line of reflection Written as: ∆ BUG  ∆ B’U’G’ a

Finding Reflection (Flip) Images In geometric terms, a reflection in line r is a transformation for which the following are true: If a point A is on line r, then the image of A is A itself If a point B is not on line r, then r is the  bisector of BB’

First locate vertices X, Y, and Z and draw XYZ in a coordinate plane. Locate points X, Y, and Z such that the line of reflection x = 4 is the perpendicular bisector of XX, YY, and ZZ. Draw the reflection image X Y Z. ∆ XYZ has vertices X(0, 3), Y(2, 0), and Z(4, 2). Draw ∆ XYZ and its reflection image in the line x = 4. Relate Reflections to the Coordinate Plane

Real-World: Using Reflection to install Security Camera Reflections Suppose you are hired by a security company to install a security camera. The camera is located as shown in the diagram. At what point on the mirrored wall should you aim the camera in order to videotape the door D? What is the line of reflection? Mirrored wall Reflect D over the mirrored wall. D’ Connect C and D’. The camera should be focused on the intersection of the segment & wall.