1. Rotations Advanced Geometry Rigid Transformations Lesson 3

2. all points of a figure a specified _______ and __________ about a fixed point. Turn Rotation angle direction http://www.mathsisfun.com/flash.php?path=%2Fgeometry/images/rotation.swf&w=670. 5&h=571.5&col=%23FFFFFF&title=Geometry+Rotation

3. To rotate a figure by hand you need: a pencil a straightedge a compass a protractor Is a rotation by hand a construction? Explain. No. A protractor is used to measure angles. Since measurements are being used, this is not a construction.

4. Draw a Rotation Example: Rotate quadrilateral ABCD 45° counterclockwise about point X. Draw a segment from X to A. Measure a 45° angle with as a side. Draw the other side. Use the compass to copy onto the new ray. Repeat this process for points B, C, and D. Connect points A', B', C', and D'.

5. Example: Triangle LMN has vertices L(-2, -1), M(-1, 2), and N(1, -1). Draw the image of ∆ LMN under a rotation of 115° clockwise about the point Y(-4, -2).

6. Common Rotations about the Origin To rotate a figure 90º counterclockwise, about the origin take each vertex and: 1. switch the coordinates 2. multiply the first coordinate (the new x) by -1 F(2, 2) G(4, 1.5) H(5, 4) F (-2, 2) G (-1.5, 4) H(-4, 5)

7. To rotate a figure 180º, multiply both coordinates by -1. R(-3, 4) S(0, 5) T(0, 1) R (3, -4) S (0, -4) T(0, -1) Q(-3, 2) Q (3, -2)

8. Example: Triangle XYZ has vertices X(-4, 1), Y(-1, 5), and Z(-6, 9). Find the coordinates of the vertices after a 90º counterclockwise rotation and graph the image.

9. Example: Rectangle ABCD has vertices A(-1, 1), B(-5, 1), C(-5, 4), and D(-1, 4). Find the coordinates of the vertices after a 180º counterclockwise rotation and graph the image.

10. Rotational Symmetry Turn the figure LESS THAN 360° so the image is the same as the pre-image. Order Magnitude the number of rotations less than 360° (including 0 °) the measure of each angle of rotation 572°