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12.6 Rotations and Symmetry Rotation- a transformation in which a figure is turned around a point Center of rotation- the point the figure is rotated around Angle of rotation- how far the figure has been rotated Figures can be rotated clockwise or counterclockwise

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Tell whether the blue shape has been rotated about the origin. If so, give the angle and direction.

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When the center of rotation is the origin and the angle of rotation is 90o there is a pattern for the coordinates.

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1.) Draw ABC withe vertices A (-3,4), B(-2,3) and C (-2,1) 2.) Find the coordinates of the vertices of the image after 90o clockwise rotation 3.) Draw the image Rotating a Triangle 90o

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To rotate a point 180o about the origin multiply each coordinate by -1. Rotating a Triangle 180o 1.) Draw a MNP with vertices M(1,-2), N (4,-1) and P(2,-3) 2.) Find the coordinates of the vertices of the image after 180o rotation 3.) Draw the image

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Rotational Symmetry - if a rotation of 1800 or less about its center produces an image that fits exactly on the original figure Example: Tell whether the figure has rotational symmetry. If so, give each angle and direction. 1.) 2.)

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12.7 Dilations Dilation - a transformation in which a figure stretches or shrinks with respect to a point called the center of dilation Scale Factor- the ratio of the side length of the image to the corresponding side length of the original To find the image coordinates, multiply the original coordinates by the scale factor.

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Dilating a Quadrilateral 1.) Draw quadrilateral ABCD with vertices A (-1,2), B(3,1), C(2,-1) and D (-1,-1) 2.) Find the coordinates of the vertices of the image after a dilation having a scale factor of 3. 3.) Draw the image

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Finding a Scale Factor Find the scale of the dilation

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Demonstrate Understanding. 1.) Draw PQR with vertices P (4,4), Q (8,0), and R (6,-2) 2.) Find the coordinates of the vertices of the image after a dilation having a scale factor of 0.5. 3.) Draw the image

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Warm Up A figure has vertices A, B, and C. After a transformation, the image of the figure has vertices A′, B′, and C′. Draw the pre-image and the image.

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