1. Rotations Rotations Rotations Rotations Rotations Rotations Rotations
Ch 9-3
Rotations
Rotations
Rotations
Rotations

2. Draw rotated images using the angle of rotation. rotation
center of rotation
angle of rotation
rotational symmetry
invariant points
direct isometry
indirect isometry
Identify figures with rotational symmetry.
Lesson 3 MI/Vocab

3. Rotations
A transformation in which a figure is turned about a fixed point.
The fixed point is the Center of Rotation
Rays drawn from the center of rotation to a point and its image form an angle called the Angle of Rotation.

4. Watch when this rectangle is rotated by a given angle measure.
Center of Rotation

5. Angle of Rotation Hi
Center of Rotation

6. A. For the following 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 A B C D
Lesson 3 CYP1

7. Rotations A composite of two reflections over two intersecting lines
The angle of rotation is twice the measure of the angle b/t the two lines of reflection
Coordinate Plane rotation
Rotating about the origin

8. Reflections in Intersecting Lines
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.
Lesson 3 Ex2

9. In the following diagram, which triangle is the image of ΔABC under reflections in line m and then line n.
A. blue Δ
B. green Δ
C. neither A B C
Lesson 3 CYP2

10. Coordinate Plane Rotation
Rotating about the origin
Clockwise vs.Counterclockwise
90o  Quarter turn
180o  Half turn (clockwise or counterclockwise)
270o  Three quarter turn
Big Hint!!!
If you need to rotate a shape about the origin,
TURN THE PAPER
Write down the new coordinates
Turn the paper back and graph the rotated points.

11. Example #1 Rotate ABC 90o clockwise about the origin. Turn the paper
Write the new coordinates C’ B’
A’ (2, 4)
B’ (4, 1)
C’ (-1, 3)
Turn the paper back and graph the rotated points

12. Example #2 Rotate ABC 180o about the origin. Turn the paper (180o)
Write the new coordinates C’
A’ (4, -2)
B’ (1, -4)
C’ (3, 1) A’ B’
Turn the paper back and graph the rotated points

13. Rotational Symmetry
A figure has rotational symmetry if it can be mapped onto itself by a rotation of 180º or less.
Equilateral Triangle
Square
Most regular polygons A B C D

14. The equilateral triangle has rotational symmetry of order = 3.
There are 3 rotations (<360 degrees) where the triangle maps onto itself.
The equilateral triangle has rotational symmetry of order = 3.
magnitude of symmetry
An equilateral triangle maps onto itself every 120 degrees of rotation.

15. An regular pentagon has an order of 5.1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
magnitude of symmetry

16. A. Rotate quadrilateral RSTV 45° counterclockwise about point A.
Draw a Rotation
A. Rotate quadrilateral RSTV 45° counterclockwise about point A.
Draw a segment from point R to point A.
Use a protractor to measure a 45° angle counterclockwise with as one side. Extend the other side to be longer than AR.
Locate point R' so that AR = AR'.
Repeat this process for points S, T, and V.
Connect the four points to form R'S'T'V'.
Lesson 3 Ex1

17. Draw a Rotation
Quadrilateral R'S'T'V' is the image of quadrilateral RSTV under a 45° counterclockwise rotation about point A.
Answer:
Lesson 3 Ex1

18. First draw ΔDEF and plot point G.
Draw a Rotation
B. 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 ΔDEF and plot point G.
Draw a segment from point G to point D.
Use a protractor to measure a 115° angle clockwise with as one side.
Draw
Use a compass to copy onto Name the segment
Repeat with points E and F.
Lesson 3 Ex1

19. Draw a Rotation
ΔD'E'F' is the image of ΔDEF under a 115° clockwise rotation about point G.
Answer:
Lesson 3 Ex1

20. B. Triangle ABC has vertices A(1, –2), B(4, –6), and C(1, –6)
B. Triangle ABC has vertices A(1, –2), B(4, –6), and C(1, –6). Draw the image of ΔABC under a rotation of 70° counterclockwise about the point M(–1, –1).
A. B.
C. D. A B C D
Lesson 3 CYP1