Chapter 12 Transformations: Shapes in Motion 12 Transformations: ... 3 Reflections A reflection (or flip) ... Section 4: Dilations/Symmetry . 58 . 59 Section 5: Compositions 1.
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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
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