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

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Presentation transcript:

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

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?

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)

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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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.

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

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

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.

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.

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.

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