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FeatureLesson Geometry Lesson Main Find the coordinates of the image point for each given point and reflection line. 1. R(4, –5) across x = –2 2. S(–11, 2) across y = 1 3. T(0, 5) across x-axis Lesson 9-2 Reflections XYZ has vertices X(–2, 3), Y(1, 1), and Z(2, 4). Draw XYZ and its reflection image in each line. 4.the x-axis5.the line x = 5 R'(–8, –5) S'(–11, 0) T'(0, 5) Lesson Quiz 9-3

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FeatureLesson Geometry Lesson Main Lesson 9-3 (For help, go to the Skills Handbook, page 746 and Lesson 1-7.) Use a protractor to draw an angle with the given measure Draw a segment, AB. Then construct A'B' congruent to AB. Rotations Check Skills Youll Need 9-3

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FeatureLesson Geometry Lesson Main Solutions Lesson 9-3 Rotations For problems 1–7, check students work. Check Skills Youll Need 9-3

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FeatureLesson Geometry Lesson Main Lesson 9-3 Rotations 9-3 To describe a rotation, you need to know the center of rotation (a point), the angle of rotation (a positive number of degrees), and whether the rotation is clockwise or counterclockwise. Unless stated otherwise, rotations in this book are counterclockwise.

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FeatureLesson Geometry Lesson Main Lesson 9-3 Rotations 9-3 You can use the following two rules to rotate a figure through x° about a point R: The image of R is itself (that is, R = R). For any point V, RV = RV and mVRV = x.

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FeatureLesson Geometry Lesson Main Lesson 9-3 Rotations 9-3 The center of a regular polygon is the point equidistant from its vertices. Segments that connect the center to the vertices divide the polygon into congruent triangles. You can use this fact to find rotation images of regular polygons.

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FeatureLesson Geometry Lesson Main 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. Lesson 9-3 Rotations Additional Examples Drawing a Rotation Image 9-3

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FeatureLesson Geometry Lesson Main Lesson 9-3 Rotations Step 3: Locate L and B in a similar manner. Then draw L O B. (continued) Quick Check Additional Examples Step 2: Use a compass to construct CO CO. 9-3

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FeatureLesson Geometry Lesson Main Regular hexagon ABCDEF is divided into six equilateral triangles. a. Name the image of B for a 240° rotation about M. b. Name the image of M for a 60° rotation about F. 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. 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. Lesson 9-3 Rotations Quick Check Additional Examples Identifying a Rotation Image 9-3

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FeatureLesson Geometry Lesson Main 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°. Lesson 9-3 Rotations Quick Check Additional Examples Finding the Angle of Rotation 9-3

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FeatureLesson Geometry Lesson Main 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. Lesson 9-3 Rotations Quick Check Additional Examples Compositions of Rotations 9-3

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FeatureLesson Geometry Lesson Main Copy RST and point C. Draw the image for the given transformation about point C. Label the vertices of the image. 1.75° rotation2.composition of a 30° rotation and then a 150° rotation Lesson 9-3 Rotations ABCDEFGH is a regular octagon. Name the image for the given rotation ° rotation of A about O G F FG 5.135° rotation of B about O 4.270° rotation of DE about O Lesson Quiz 9-3

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