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Unit Overview

Section 12-3 Transformations - Rotations SPI 32D: determine whether the plane figure has been reflected given a diagram and vice versa. Objectives: Draw and identify rotation images of figures. Unit Overview. Investigate Transformations

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Unit Overview

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  1. Section 12-3 Transformations - Rotations SPI 32D: determine whether the plane figure has been reflected given a diagram and vice versa • Objectives: • Draw and identify rotation images of figures Unit Overview • Investigate Transformations • Reflections (this lesson) • Translations • Rotations • Composition of Transformations

  2. Rotations • Type of transformation that turns a figure about a fixed point • Center of Rotation: fixed point • An object and its rotation are the same shape and size, but the figures may be turned in different directions. Rotation of a polar star taken during a 40-minute exposure by a camera.

  3. Examples of Rotations Riding a ferris wheel is an example of rotation Planetary movement is a rotation.

  4. Describing a Rotation • Need to know: • Center of rotation (a point) • Angle of rotation (number of degrees) • Whether rotation is clockwise or counterclockwise

  5. Geometric Definition of Rotation A rotation of xº about a point R is a transformation for which the following is true.

  6. Drawing a Rotation Image Copy ∆LOB, and draw its image under a 60° rotation about C. Step 1: Use a protractor to draw a 60° angle at vertex C with one side CO.

  7. … continued Step 2: Use a compass to construct CO’CO. Step 3: Locate L’ and B’ in a similar manner. Then draw L’ O’ B’ .

  8. Identify a Rotation Image Regular hexagon ABCDEF is divided into six equilateral triangles. a. Name the image of B for a 240° rotation about M. a. Because 360° ÷ 6 = 60°, each central angle of ABCDEF measures 60. A 240° counterclockwise rotation about center M moves point B across four triangles. The image of point B is point D. b. Name the image of M for a 60° rotation about F. b. AMF is equilateral, so AFM has measure 180 ÷ 3 = 60. A 60° rotation of AMF about point F would superimpose FM on FA, so the image of M under a 60° rotation about point F is point A.

  9. Identify a Rotation Image A regular 12-sided polygon can be formed by stacking congruent square sheets of paper rotated about the same center on top of each other. Find the angle of rotation about M that maps W to B. Consecutive vertices of the three squares form the outline of a regular 12-sided polygon. 360 ÷ 12 = 30, so each vertex of the polygon is a 30° rotation about point M. You must rotate counterclockwise through 7 vertices to map point W to point B, so the angle of rotation is 7 • 30°, or 210°.

  10. Compositions of Rotations Describe the image of quadrilateral XYZW for a composition of a 145° rotation and then a 215° rotation, both about point X. The two rotations of 145° and 215° about the same point is a total rotation of 145° + 215°, or 360°. Because this forms a complete rotation about point X, the image is the preimage XYZW.

  11. Rotation Web Site Link

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