1. Lesson 9.3 Rotations Key Terms
Rotation- a transformation that turns every point of a preimage through a specified angle and direction about a fixed point (called the center of rotation)
Angle of rotation- angle through which a preimage is rotated to form the image
Rotational symmetry- if a figure can be rotated less than 360° about a point so that the image and the preimage are indistinguishable, the figure has rotational symmetry.

2. Key Concept
Postulate 9.1- In a given rotation, if A is the preimage, A” is the image, and P is the center of rotation is twice the measure of the acute or right angle formed by the intersecting lines of reflection
Corollary 9.1- Reflecting an image successfully in two perpendicular lines results in a 180° rotation.

3. First draw DEF and plot point G.
Triangle DEF has vertices D(–2, –1), E(–1, 1), and F(1, –1). Draw the image of DEF under a rotation of 115° clockwise about the point G(–4, –2).
First draw DEF and plot point G. D E F
Draw a segment from point G to point D. G
Use a protractor to measure a 115° angle clockwise with as one side.
115 D'
Draw E'
Use a compass to copy onto Name the segment R F'
Repeat with points E and F.
Example 3-1a

4. D'E'F' is the image of DEF under a 115° clockwise rotation about point G.
Answer: D E F F' D' E'
Example 3-1a

5. 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 ABC under a rotation of 70° counterclockwise about the point M(–1, –1).
Answer:
Example 3-1b

6. Next, reflect the image in line q. Then label the image W''X''Y''Z''.
Find the image of parallelogram WXYZ under reflections in line p and then line q.
First reflect parallelogram WXYZ in line p. Then label the image W'X'Y'Z'.
Next, reflect the image in line q. Then label the image W''X''Y''Z''.
Answer:
Parallelogram W''X''Y''Z'' is the image of parallelogram WXYZ under reflections in line p and q.
Example 3-2a

7. Find the image of ABC under reflections in line m and then line n.
Answer:
Example 3-2b

8. QUILTS Use the quilt by Judy Mathieson shown below
QUILTS Use the quilt by Judy Mathieson shown below. Identify the order and magnitude of the symmetry in the medium star directly to the left of the large star in the center of the quilt.
Answer: The medium star directly to the left of the large star in the center has rotational symmetry of order 16 and a magnitude of 22.5°.
Example 3-3a

9. QUILTS Use the quilt by Judy Mathieson shown below
QUILTS Use the quilt by Judy Mathieson shown below. Identify the order and magnitude of the symmetry in the tiny star above the medium-sized star in Example 3a.
Answer: The tiny star has rotational symmetry of order 8 and magnitude of 45°.
Example 3-3a

10. a. star in the upper left corner
QUILTS Use the quilt by Judy Mathieson shown below. Identify the order and magnitude of the symmetry in each part of the quilt.
a. star in the upper left corner
Answer: 8; 45°
b. medium-sized star directly in center of quilt
Answer: 20; 18°
Example 3-3b