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

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

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

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

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

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.)

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.

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

Finding a Scale Factor Find the scale of the dilation

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 ) Draw the image