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Concept

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Example 1 Draw a Rotation Use a protractor to measure a 45° angle counterclockwise with as one side. Extend the other side to be longer than AR. Draw a segment from point R to point A. Locate point R ' so that AR = AR'. Rotate quadrilateral RSTV 45° counterclockwise about point A. Repeat this process for points S, T, and V. Connect the four points to form R'S'T'V'.

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Example 1 Draw a Rotation Quadrilateral R'S'T'V' is the image of quadrilateral RSTV under a 45° counterclockwise rotation about point A. Answer:

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A.A B.B C.C D.D Example 1 A.20° clockwise B.20° counterclockwise C.90° clockwise D.90° counterclockwise For the following diagram, which description best identifies the rotation of triangle ABC around point Q?

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Concept

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Example 2 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. Use a protractor to measure a 115° angle clockwise with as one side. Use a compass to copy onto Name the segment Draw Repeat with points E and F. Draw a segment from point G to point D.

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Example 2 Rotations in the Coordinate Plane Answer:ΔD'E'F' is the image of ΔDEF under a 115° clockwise rotation about point G.

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A.A B.B C.C D.D Example 2 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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Example 3 Hexagon DGJTSR is shown below. What is the image of point T after a 90 counterclockwise rotation about the origin? A (5, –3) B (–5, –3) C (–3, 5) D (3, –5)

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Example 3 Read the Test Item You are given a graph of hexagon DGJTSR and asked to identify the coordinates of the image of point T after a 90° counterclockwise rotation about the origin. Solve the Test Item To find the coordinates of point T after a 90 counterclockwise rotation about the origin, multiply the y-coordinate by –1 and then interchange the x- and y-coordinates. (x, y) → (–y, x) (5, 3) → (–3, 5) Answer: The answer is C, (–3, 5).

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A.A B.B C.C D.D Example 3 A.(–5, –4) B.(–5, 4) C.(5, 4) D.(4, –5) Triangle PQR is shown below. What is the image of point Q after a 90° counterclockwise rotation about the origin?

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Quiz Determine the slope of each line. 1. PQ 2. MN 3. Which pair of lines are parallel? In the figure, WXYZ ABCD 4. Find XY. 5. Find mB.

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