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9-3 Rotations You identified rotations and verified them as congruence transformations. Draw rotations. Draw rotations in the coordinate plane.

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**How Many Degrees… …are in a half turn? …are in a quarter turn?**

180° 90° 270° …are in a half turn? …are in a quarter turn? …three quarters turn?

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Definition A rotation is a transformation that turns a set of points about one point, the center of rotation. The pre-image and image of any point are the same distance from the center of rotation. P (Pre-image) 45° Angle of rotation Q Center of rotation P’ (Image)

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Definition continued The angle of rotation measures how much a point is turned about the center. For example, if point P is rotated 45° clockwise about center of rotation Q, Q P (Pre-image) P’ (Image) Center of rotation Angle of rotation 45°

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p. 640

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Draw a Rotation Rotate quadrilateral RSTV 45° counterclockwise about point A. Draw a segment from point R to point A. Use a protractor to measure a 45° angle counterclockwise with as one side. Extend the other side to be longer than AR. Answer: Locate point R' so that AR = AR'. Repeat this process for points S, T, and V. Connect the four points to form R'S'T'V'. Quadrilateral R'S'T'V' is the image of quadrilateral RSTV under a 45° counterclockwise rotation about point A.

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**For the diagram, which description best identifies the rotation of triangle ABC around point Q?**

A. 20° clockwise B. 20° counterclockwise C. 90° clockwise D. 90° counterclockwise

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**When a point is rotated 90°, 180°, or 270° counterclockwise around (0,0), you can use these rules:**

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**Spin It When will the image exactly overlap the pre-image?**

30° clockwise 60°clockwise 90°clockwise 120°clockwise If a figure can be rotated onto itself with an angle or rotation between 0° and 360 °, the figure has rotational symmetry.

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**Rotations in the Coordinate Plane**

Triangle DEF has vertices D(–2, –1), E(–1, 1), and F(1, –1). Graph ΔDEF and its image after a rotation of 115° clockwise about the point G(–4, –2). First, draw ΔDEF and plot point G. Draw a segment from point G to point D. Use a protractor to measure a 115° angle clockwise with as one side. Answer: Draw Use a compass to copy onto Name the segment Repeat with points E and F. ΔD'E'F' is the image of ΔDEF under a 115° clockwise rotation about point G.

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**Triangle ABC has vertices A(1, –2), B(4, –6), and C(1, –6)**

Triangle ABC has vertices A(1, –2), B(4, –6), and C(1, –6). Draw the image of ΔABC under a rotation of 70° counterclockwise about the point M(–1, –1). A. B. C. D.

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9-3 Assignment Page 643, 6-10 even, 11-13, 14-18

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Objective: Students will be able to represent translations, dilations, reflections and rotations with matrices.

Objective: Students will be able to represent translations, dilations, reflections and rotations with matrices.

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