Chapter 12

Transformations:

Shapes in Motion

Table of Contents

Reflections – Day 1 ……………………………………………..…………….. Page 1

SWBAT: Graph Reflections in the Coordinate Plane

HW: Pages #8 - 10

Translations – Day 2 ……………….……….…………….……..…………….. Page 11

SWBAT: Graph Translations in the Coordinate Plane

HW: Pages #15 - 16

Rotations – Day 3…………………………………………..………………….. Page 17

SWBAT: Graph Rotations in the Coordinate Plane

HW: Pages #23-24

Dilations/Symmetry – Day 4 …………………………………………….….….. Page 25

SWBAT: Graph Dilations in the Coordinate Plane and Identify Line/Rotational Symmetry

HW: Pages #31-34

Review – Day 5 ……………………………………………..……..…………….. Page 35

SWBAT: Graph Transformations in the Coordinate Plane

HW: Pages #35-38

Compositions – Day 6……………………..……………………………….…….. Page 39

SWBAT: Graph Compositions in the Coordinate Plane

HW: Pages #46-49

Overall Review – Day 7……………………….………………………..………….. Page 50

SWBAT: Graph Transformations in the Coordinate Plane

HW: Pages #50-61

TRANSFORMATIONS RULES ………….…………………………………………..Page 62

1

Reflections – Day 1

An Introduction to Transformations

2

Example 1:

Example 2:

3

Reflections A reflection (or flip) is an isometry in which a figure

and its image have opposite orientations.

Thus, a reflected image in a mirror appears "backwards."

Reflections in the Coordinate Plane

1.

4

Regents Questions

5. 6.

7. 8.

3. 4.

5

Reflecting Over Vertical and Horizontal Lines

9.

10.

6

Identifying a Reflection Write a rule to describe each transformation.

11. 12.

Challenge

7

Summary

Exit Ticket

8

Homework for Reflections – Day 1

16.

17.

9

Graphing Reflections

10

Identifying Reflections

11

Translations – Day 2

Warm - Up

1.

2.

12

3. 4.

5.

6.

13

You Try It!

1) Triangle DEF is a translation of triangle ABC. Use the diagram to write a rule for the

translation of triangle ABC to Triangle DEF.

2) Pentagon ABCDE is drawn on the grid below.

On the grid, draw a translation of pentagon ABCDE using the rule T3,-5.

14

Challenge

Summary

Exit Ticket

15

Homework

16

16. T5,1 17. T-1, 2

18. T0, -3 19. T4, -4

17

Rotations – Day 3

Warm - Up

1.

2.

18

Notice that degree movement on a unit circle goes in a

counterclockwise direction. You will want to remember the layout of

the unit circle when you are graphing figures and their rotations.

19

Rules

(x, y)

R90 = ( ___, ____)

R180 = ( ___, ____)

R270 = ( ___, ____)

Practice

3. 4. 5.(9, -1) (-4, -8)

20

Rotations in the Coordinate Plane

9.

10.

***NOTE

X’( ___, ____) Y’( ___, ____) Z’( ___, ____)

90

90

180

180

21

Practice with a Point Reflection in the Origin

Identifying a Rotation Write a rule to describe each transformation.

a. b.

22

Challenge

Summary

Exit Ticket

23

Homework

24

25

Dilations/Symmetry – Day 4

Warm – Up

1. 2.

26

To find the image of a point under a dilation, you multiply each coordinate by the

scale factor.

a) D4 (x,y) (4x,4y) b) D6

1(x,y) ( Yx

6

1,

6

1)

Example- Find a) D2(3,4)

b)

31

D (6,9)

Dilations in the Coordinate Plane

1.

27

2.

Regents Questions

3.

4.

5.

6.

7.

28

29

Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry.

Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry.

30

Challenge

SUMMARY

31

Homework – Dilations/Symmetry – Day 4

32

22.

23.

33

Symmetry

34

35

Review – Day 5

36

37

38

39

Compositions – Day 6

Warm – Up

1.

2.

Which rotation about point O maps B to D? _______

40

c)

41

Practice Problem #1

You try It!

42

Practice Problem #2

You try It!

43

The symbol for a composition of transformations is an open circle.

The notation is read as a reflection in the x-axis following a

translation of (x+3, y+4). Be careful!!! The process is done in reverse!!

You may see various notations which represent a composition of transformations:

could also be indicated by

Problem #3

44

You Try It!

CHALLENGE

45

SUMMARY

Exit Ticket

46

Homework – Compositions – Day 6

1.

2.

3.

47

4.

5.

6.

7. 7.

48

8.

9.

49

10.

50

Review – Day 7

Transformations Review SUMMARY TABLE

51

Section 1: Reflections

52

Line Reflections

53

Section 2: Translations

54

55

Section 3: Rotations

3. Locate and label A’, the image of A under R270 (three quarter-turn about the origin)

56

57

Section 4: Dilations/Symmetry

58

59

Section 5: Compositions 1.

2. fdg

3.

4.

5. Find the composite transformation indicated.

60

6.

7.

61

8. *** Other Properties***

5.

62