9.3 Rotations Then: You identified rotations and verified them as congruence transformations. Now: You will draw rotations in the coordinate plane.

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Presentation transcript:

9.3 Rotations Then: You identified rotations and verified them as congruence transformations. Now: You will draw rotations in the coordinate plane. http://now.tufts.edu/sites/default/files/110919_ASK_windmill_L.JPG

I. Rotation A. A transformation that turns every point of a preimage through a specified angle and direction about a fixed point, called the center of rotation. B. A rotation about a fixed point through an angle of x is a function that maps a point to its image such that 1. if the point is the center of rotation, then the image and preimage are the same point, or https://s-media-cache-ak0.pinimg.com/236x/06/33/ae/0633aea2d8370fcf5ba8e5940c480c8d.jpg

I. Rotation 2. if the point is not the center of rotation, then the image and the preimage are the same distance from the center of rotation and the measure of the angle of rotation formed by the preimage, center of rotation, and image points is x. http://www.freelearningchannel.com/l/Content/Materials/Mathematics/Geometry/textbooks/CK12_Geometry/html/12/ck12_4_files/20130325223109703317.png

I. Rotation 3. 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

I. Rotation 4. Draw the image of ABCD under a 180° clockwise rotation about the origin. A. B. C. D.

II. Rotation in Coordinate Plane A. Rules for counterclockwise rotations about the origin. 1.

II. Rotation in Coordinate Plane 2. 3.

II. Rotation in Coordinate Plane B. Graph each figure and its image after the specified rotation about the origin. 1. Triangle LMN has vertices L (-1, -1), M(0, -4), and N(-6, -2); 90 Rule: L’ (_____, _____) M’ (_____, _____) N’ (_____, _____)

II. Rotation in Coordinate Plane B. Graph each figure and its image after the specified rotation about the origin. 2. Triangle ABC has vertices A(-3, 5), B(0, 2) and C(-5, 1); 180 Rule: A’ (_____, _____) B’ (_____, _____) C’ (_____, _____)

II. Rotation in Coordinate Plane B. Graph each figure and its image after the specified rotation about the origin. 3. Parallelogram PQRS has vertices P(4, 7), Q(6, 6), R(3, -2) and S(1, -1); 270 Rule: P’ (_____, _____) Q’ (_____, _____) R’ (_____, _____) S’ (_____, _____)

9.3 Assignment P. 643-646 #11-21 all, 24-26 all, 39-42 all, 47-49 all Graph: 14-19, 24-26- need 2 sheets of graph paper.