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
Reflections – Day 1
An Introduction to Transformations
1
Example 1:
Example 2:
2
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.
3
3. 4.
Regents Questions
5. 6.
7. 8.
4
Reflecting Over Vertical and Horizontal Lines
9.
10.
5
Identifying a Reflection Write a rule to describe each transformation. 11. 12.
Challenge
6
Summary
Exit Ticket
7
Homework for Reflections – Day 1
16.
17.
8
Graphing Reflections
9
Identifying Reflections
10
Translations – Day 2
Warm - Up
1.
2.
11
3. 4.
5.
6.
12
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.
13
Challenge
Summary
Exit Ticket
14
Homework
15
16. T5,1 17. T-1, 2
18. T0, -3 19. T4, -4
16
Rotations – Day 3
Warm - Up
1.
2.
17
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.
18
Rules (x, y)
R90 = ( ___, ____)
R180 = ( ___, ____)
R270 = ( ___, ____)
Practice
3. 4. ( 9, -1) 5. (-4, -8)
19
Rotations in the Coordinate Plane
9. 90 X’( ___, ____) Y’( ___, ____) Z’( ___, ____)
90
10. 180
180
***NOTE
20
Practice with a Point Reflection in the Origin
Identifying a Rotation Write a rule to describe each transformation.
a. b.
21
Challenge
Summary
Exit Ticket
22
Homework
23
24
Dilations/Symmetry – Day 4
Warm – Up
1. 2.
25
To find the image of a point under a dilation, you multiply each coordinate by the scale factor.
1 1 1 a) D4 (x,y) (4x,4y) b) D (x,y) ( x, Y ) 6 6 6
Example- Find a) D2(3,4)
b) D (6,9) 1 3
Dilations in the Coordinate Plane
1.
26
2.
Regents Questions
3.
4.
5.
6.
7.
27
28
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.
29
Challenge
SUMMARY
30
Homework – Dilations/Symmetry – Day 4
31
22.
23.
32
Symmetry
33
34
Review – Day 5
35
36
37
38
Compositions – Day 6
Warm – Up
1.
2.
Which rotation about point O maps B to D? ______
39
c)
40
Practice Problem #1
You try It!
41
Practice Problem #2
You try It!
42
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
43
You Try It!
CHALLENGE
44
SUMMARY
Exit Ticket
45
Homework – Compositions – Day 6
1.
2.
3.
46
4.
5.
6.
7. 7.
47
8.
9.
48
10.
49
Review – Day 7 Transformations Review
SUMMARY TABLE
50
Section 1: Reflections
51
Line Reflections
52
Section 2: Translations
53
54
Section 3: Rotations
3. Locate and label A’, the image of A under R270 (three quarter-turn about the origin)
55
56
Section 4: Dilations/Symmetry
57
58
Section 5: Compositions
1.
2. fdg
3.
4.
5. Find the composite transformation indicated.
59
6.
7.
60
8.
*** Other Properties***
5.
61
62