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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
Compositions – Day 5……………………………………………..……..…………….. Page 35
SWBAT: Graph Compositions in the Coordinate Plane
HW: Pages #35-38
Overall Review – Day 6……………………..……………………………….…….. Page 39
SWBAT: Graph Compositions in the Coordinate Plane
HW: Pages #46-49
TRANSFORMATIONS RULES ………….…………………………………………..Page 62
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.
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.
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.(2, 3) (-1, 6) (-7, -4)
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.
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.
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.
39
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
47
Transformations Review
Translations
1.
2.
3.
Reflections
4.
5. What is the image of (-4, -6) when reflected in the x-axis?
6. What are the coordinates of the point (-2, 7) after a reflection in the line y = 3?
7. What are the coordinates of the point (4, 12) after a reflection in the line x = 3?
48
Rotations
1. 2.
3. If point P(-5, 3) is rotated 270 about the origin, what is the image of P?
Dilations 1. 2. 3.