1. Find the coordinates of the image point for each given point and
Reflections
Lesson 9-2
Lesson Quiz
Find the coordinates of the image point for each given point and
reflection line.
1. R(4, –5) across x = –2
2. S(–11, 2) across y = 1
3. T(0, 5) across x-axis
R'(–8, –5)
S'(–11, 0)
T'(0, 5)
XYZ has vertices X(–2, 3), Y(1, 1), and Z(2, 4). Draw XYZ
and its reflection image in each line.
4. the x-axis 5. the line x = 5
9-3

2. Use a protractor to draw an angle with the given measure.
Rotations
Lesson 9-3
Check Skills You’ll Need
(For help, go to the Skills Handbook, page 746 and Lesson 1-7.)
Use a protractor to draw an angle with the given measure.
7. Draw a segment, AB. Then construct A'B' congruent to AB.
Check Skills You’ll Need
9-3

3. For problems 1–7, check students’ work.
Rotations
Lesson 9-3
Check Skills You’ll Need
Solutions
For problems 1–7, check students’ work.
9-3

4. Rotations
Lesson 9-3
To describe a rotation, you need to know the center of rotation (a point), the angle of rotation (a positive number of degrees), and whether the rotation is clockwise or counterclockwise. Unless stated otherwise, rotations in this book are counterclockwise.
9-3

5. You can use the following two rules to
Rotations
Lesson 9-3
You can use the following two rules to
rotate a figure through x° about a point R:
• The image of R is itself (that is, R’ = R).
• For any point V, RV’ = RV and mVRV’ = x.
9-3

6. Rotations
Lesson 9-3
The center of a regular polygon is the point equidistant from its vertices.
Segments that connect the center to the vertices divide the polygon into congruent triangles. You can use this fact to find rotation images of regular polygons.
9-3

7. Drawing a Rotation Image
Rotations
Lesson 9-3
Additional Examples
Drawing a Rotation Image
Copy LOB, and draw its image under a 60° rotation about C.
Step 1: Use a protractor to draw a 60° angle at vertex C with one side CO.
9-3

8. Step 2: Use a compass to construct CO CO.
Rotations
Lesson 9-3
Additional Examples
(continued)
Step 2: Use a compass to construct CO CO.
Step 3: Locate L and B in a similar manner. Then draw L O B .
Quick Check
9-3

9. Identifying a Rotation Image
Rotations
Lesson 9-3
Additional Examples
Identifying a Rotation Image
Regular hexagon ABCDEF is divided into six equilateral triangles.
a. Name the image of B for a 240° rotation about M.
b. Name the image of M for a 60° rotation about F.
a. Because 360° ÷ 6 = 60°, each central angle of ABCDEF measures 60. A 240° counterclockwise rotation about center M moves point B across four triangles. The image of point B is point D.
b AMF is equilateral, so AFM has measure 180 ÷ 3 = 60. A 60° rotation of AMF about point F would superimpose FM on FA, so the image of M under a 60° rotation about point F is point A.
Quick Check
9-3

10. Finding the Angle of Rotation
Rotations
Lesson 9-3
Additional Examples
Finding the Angle of Rotation
A regular 12-sided polygon can be formed by stacking congruent square sheets of paper rotated about the same center on top of each other. Find the angle of rotation about M that maps W to B.
Consecutive vertices of the three squares form the outline of a regular 12-sided polygon.
360 ÷ 12 = 30, so each vertex of the polygon is a 30° rotation about point M.
You must rotate counterclockwise through 7 vertices to map point W to point B, so the angle of rotation is 7 • 30°, or 210°.
Quick Check
9-3

11. Compositions of Rotations
Lesson 9-3
Additional Examples
Compositions of Rotations
Describe the image of quadrilateral XYZW for a composition of a 145° rotation and then a 215° rotation, both about point X.
The two rotations of 145° and 215° about the same point is a total rotation of 145° + 215°, or 360°.
Because this forms a complete rotation about point X, the image is the preimage XYZW.
Quick Check
9-3

12. Copy RST and point C. Draw the image for the given
Rotations
Lesson 9-3
Lesson Quiz
Copy RST and point C. Draw the image for the given
transformation about point C. Label the vertices of the image.
1. 75° rotation
2. composition of a 30° rotation and then a 150° rotation
ABCDEFGH is a regular octagon.
Name the image for the given rotation.
3. 135° rotation of A about O F
4. 270° rotation of DE about O FG
5. 135° rotation of B about O G
9-3