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Lesson 9-3

Lesson 9-3. Rotations or Turns. Transparency 9-3. R’(3,-4), S’(-1,1). G’(-1,0), H’(-2,-3), I’(-5,-4), J’(-5,3). A’(-1,-1), B’(1,-3), C’(3,1). L’(1,5), M’(4,5), N’(0,-1), O’(-1,2). (x, y)  (x + 3, y – 2). D. 5-Minute Check on Lesson 9-2.

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Lesson 9-3

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  1. Lesson 9-3 Rotations or Turns

  2. Transparency 9-3 R’(3,-4), S’(-1,1) G’(-1,0), H’(-2,-3), I’(-5,-4), J’(-5,3) A’(-1,-1), B’(1,-3), C’(3,1) L’(1,5), M’(4,5), N’(0,-1), O’(-1,2) (x, y)  (x +3, y – 2) D 5-Minute Check on Lesson 9-2 • Find the coordinates of each figure under the given translation. • RS with endpoints R(1,-3) and S(-3,2) under the translation right 2 units and down 1 unit. • Quadrilateral GHIJ with G(2,2), H(1,-1), I(-2,-2), and J(-2,5) under the translation left 2 units and down 3 units. • ∆ABC with vertices A(-4,3), B(-2,1), and C(0,5) under the translation (x, y)  (x + 3, y – 4) • Trapezoid LMNO with vertices L(2,1), M(5,1), N(1,-5), and O(0-2) under the translation (x, y)  (x – 1, y + 4) • Find the translation that moves AB with endpoints A(2,4) and B(-1,-3) to A’B’ with endpoints A’(5,2) and B’(2,-5) • Which describes the translation left 3 units and up 4 units? Standardized Test Practice: (x, y)  (x + 3, y – 4) (x, y)  (x –3, y – 4) A B (x, y)  (x + 3, y + 4) (x, y)  (x –3, y + 4) C D Click the mouse button or press the Space Bar to display the answers.

  3. Objectives • Draw rotated images using the angle of rotation • Identify figures with rotational symmetry

  4. Vocabulary • Rotation – transformation that turns every point of a pre-image through a specified angle and direction about a fixed point • Center of rotation – fixed point of the rotation • Angle of rotation – angle between a pre-image point and corresponding image point • Rotational symmetry – a figure can be rotated less than 360° so that the pre-image and image look the same (indistinguishable) • Order – number of times figure can be rotated less than 360° in above • Magnitude – angle of rotation (360° / order)

  5. E D F Use a protractor to measure a 115° angle clockwise with as one side. 115 Draw Use a compass to copy onto Name the segment Example 3-1a Triangle DEF has vertices D(–2, –1),E(–1, 1), and F(1, –1). Draw the image of DEF under a rotation of 115° clockwise about the point G(–4, –2). First draw DEF and plot point G. Draw a segment from point G to point D. G D' E' R F' Repeat with points E and F.

  6. E D D' F E' F' Example 3-1a D'E'F' is the image of DEF under a 115° clockwise rotation about point G. Answer:

  7. Example 3-1b Triangle ABC has vertices A(1, –2),B(4, –6), and C(1, –6). Draw the image of ABC under a rotation of 70° counterclockwise about the point M(–1, –1). Answer:

  8. Example 3-2a Find the image of parallelogram WXYZ under reflections in line pand then line q. First reflect parallelogram WXYZ in line p. Then label the image W'X'Y'Z'. Next, reflect the image in line q. Then label the image W''X''Y''Z''. Answer: Parallelogram W''X''Y''Z'' is the image of parallelogram WXYZ under reflections in line p and q.

  9. Example 3-2b Find the image of ABCunder reflections in line mand then line n. Answer:

  10. y B’ C’ A’ x angle of rotation(90°) point of rotation(origin) Rotation Rotation – a transformation that turns all points of a figure, through a specified angle and direction about a fixed point A A (2,7) B (8,4) C (3,3) In Powerpoint:the free rotate (green dot) allowsrotation, but onlyaround the figure’scenter point – notan outside point B C Each point rotated90° to the left (counter clockwise) around the origin 180° Rotation – reflection across the origin!

  11. Example 3-3a QUILTS Use the quilt by Judy Mathieson shown below. Identify the order and magnitude of the symmetry in the medium star directly to the left of the large star in the center of the quilt. Answer: The medium star directly to the left of the large star in the center has rotational symmetry of order 16 and a magnitude of 22.5°.

  12. Example 3-3a QUILTS Use the quilt by Judy Mathieson shown below. Identify the order and magnitude of the symmetry in the tiny star above the medium-sized star in Example 3a. Answer: The tiny star has rotational symmetry of order 8 and magnitude of 45°.

  13. Example 3-3b QUILTS Use the quilt by Judy Mathieson shown below. Identify the order and magnitude of the symmetry in each part of the quilt. a. star in the upper left corner Answer: 8; 45° b. medium-sized star directly in center of quilt Answer: 20; 18°

  14. Rotational Symmetry Rotational Symmetry – if a figure can be rotated less than 360° and the image and pre-image are indistinguishable (regular polygons are a great example) Order: 3 4 6 8 Magnitude: 120° 90° 60° 45° Remember Order = n (number of sides) and Magnitude = 360 / Order

  15. Summary & Homework • Summary: • A rotation turns each point in a figure through the same angle about a fixed point • An object has rotational symmetry when you can rotate it less than 360° and the pre-image and the image are indistinguishable (can’t tell them apart) • Homework: • pg 479-481; 9, 10, 14, 15, 23, 41

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