This document is a lesson on rotations of 180 degrees. It discusses the rule for rotating a point (x,y) 180 degrees, which is that it maps to (-x,-y). Examples are given of rotating points and figures 180 degrees clockwise and counterclockwise. The lesson emphasizes that rotating 180 degrees clockwise or counterclockwise yields the same result. Practice problems have students rotating triangles and finding the images of points under a 180 degree rotation. Other rotation rules for 90 degrees are also stated.

1. Module 8.2 Lesson 6 Rotations of 180 degrees.notebook
1
May 10, 2016
HW
p 62-63 # 7, 9, 10
Module 8.2 Lesson 6
Rotations of 180 degrees
Do Now:
The measure of a supplement of an
angle is 390
more than half the
angle. Find the angles.

2. Module 8.2 Lesson 6 Rotations of 180 degrees.notebook
2
May 10, 2016
5.
Homework p 52 #5

3. Module 8.2 Lesson 6 Rotations of 180 degrees.notebook
3
May 10, 2016
6.
Homework p 52 #6

4. Module 8.2 Lesson 6 Rotations of 180 degrees.notebook
4
May 10, 2016
7.

5. Module 8.2 Lesson 6 Rotations of 180 degrees.notebook
5
May 10, 2016

6. Module 8.2 Lesson 6 Rotations of 180 degrees.notebook
6
May 10, 2016
Page 55

7. Module 8.2 Lesson 6 Rotations of 180 degrees.notebook
7
May 10, 2016
(­4,3)
(4,­3)
(x,y) (­x,­y)
Rule:
Page 55

8. Module 8.2 Lesson 6 Rotations of 180 degrees.notebook
8
May 10, 2016
Rules for Rotating 180 degrees
(x,y) (­x,­y)
** Rotating a figure 180 degrees clockwise is the same as
rotating a figure 180 degrees counter clockwise!!

9. Module 8.2 Lesson 6 Rotations of 180 degrees.notebook
9
May 10, 2016
(x,y) (­x,­y)
(2, ­4) (­2, 4)
**Start to rotate
counter-clockwise
Page 56

10. Module 8.2 Lesson 6 Rotations of 180 degrees.notebook
10
May 10, 2016
Page 56
(x,y) (­x,­y)
(-3,5) --> (3,-5)

11. Module 8.2 Lesson 6 Rotations of 180 degrees.notebook
11
May 10, 2016
(­6,6)
Page 57

12. Module 8.2 Lesson 6 Rotations of 180 degrees.notebook
12
May 10, 2016
Page 57

13. Module 8.2 Lesson 6 Rotations of 180 degrees.notebook
13
May 10, 2016
Pre­Image Image
A (1, 2)
B (4, 6)
C (7, 1)
A' (­1, ­2)
B' (­4, ­6)
C' (­7, ­1)
A'
B'
C'
Page 57

14. Module 8.2 Lesson 6 Rotations of 180 degrees.notebook
14
May 10, 2016
U (2, 4)
R (4, 8)
S (6, 4)
O (4, ­2)
U
R
O
S
Page 62

15. Module 8.2 Lesson 6 Rotations of 180 degrees.notebook
15
May 10, 2016
U (2, 4)
R (4, 8)
S (6, 4)
O (4, ­2)
O'
U
R
O
S
U (­2, ­4)
R (­4, ­8)
S (­6, ­4)
O (­4, 2)
S' U'
R'
Page 62

16. Module 8.2 Lesson 6 Rotations of 180 degrees.notebook
16
May 10, 2016
11.
the origin
A
B C
Page 63

17. Module 8.2 Lesson 6 Rotations of 180 degrees.notebook
17
May 10, 2016
11.
the origin
A
B C
A' (­4, ­3)
B' (­4, ­6)
C' (­7, ­6)
A (4, 3)
B (4, 6)
C (7, 6)
A'
B'C'
Page 63

18. Module 8.2 Lesson 6 Rotations of 180 degrees.notebook
18
May 10, 2016
Triangle ABC
A (1, 2)
B (1,7)
C (4,2)
Reflection over y = -x
A`
B`
C`

19. Module 8.2 Lesson 6 Rotations of 180 degrees.notebook
19
May 10, 2016
Rules for Rotations
90 degrees clockwise: (x,y) (y,-x)
90 degrees counter clockwise: (x,y) (-y,x)
180 degrees: (x,y) (-x,-y)

20. Module 8.2 Lesson 6 Rotations of 180 degrees.notebook
20
May 10, 2016

21. Module 8.2 Lesson 6 Rotations of 180 degrees.notebook
21
May 10, 2016