Name: ___________________
Transformations Test
Warm Up:
1. Graph the line y = 2x – 4
2. Move the graph of the line up 3 units
3. Write the equation of the graph
you just created:
4. How are these two graphs related?
5. Now graph the line y = - ½ x – 4
6. How are the graphs for 1 and 5 related?
PowerPoint Presentation
Transformation Type
Definition
Example
Real World
Translation
Reflection
Rotation
Notes and Examples:

The new figure is called the _____________________

The original figure is called the ________________________

If the pre-image point is A, then the image point is ______________________

Instead of saying Triangle ABC was “mapped onto” Triangle A’B’C’, You can also use
______________________ notations: Triangle ABCTriangle A’B’C’

An ______________________is a transformation that preserves lengths,
distances, and angle measurements, and parallel lines
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Recognizing the type of transfromation that occurred:
1.
2.
3.
4.
Example 1: Transformation using “directions” Example 2: Transformation using vector:
Translate <x-5, y+3>
D
Example 3: Reflections about the x- axis
Example 4: Reflections about x = -3
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Unit 2 Lesson 4
Name: ______________________
Translations and Reflections Practice
Hour: _______________________
1. What is the name of this symbol: A’
2. A’ would be used to indicate a point on the image or pre-image?
3. Which transformations are isometries? Which are not?
4. What type of transformation would change b into p?
5. What type of transformation would change b into q?
6. What type of transformation would change b into b?
8. Use the vector to
translate the point.
9.
Translate  x + 2, y - 3 
U
S
R
T
P
O
N
10. TranslatePoint T
using the mapping
MB.
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
X
Y
Z
11. What vector translates the
dotted figure onto the solid
figure.
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12 Reflect the figure across
the line y = 2.
13. Reflect the figure across
line
M
I
D
N
14. Reflect the figure
across line l
l
O
l
N
R
T
l
A
P
15. Reflect the figure across
the y axis.
16.
Reflect the figure across
line l
17. Draw the line of
reflection for the
figures.
O
O
l
B
Y
T
Y
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18. Reflect D across each of the following and give the coordinates of each image.
a. x axis
b. y axis
c. y = 2
d. x = -1
e. y = x
f. y = -x
a.
.
b.
D
D
D=
D’=
c.
D=
D’=
d.
D
D
D=
D’=
e.
D
D=
D’=
D=
f.
D’=
D
D=
D’=
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RALLY COACH: Start with the shoulder partner with the lowest birthday month
A
B
RULE: (x, y)(x+2, y-3)
Translate according to the
given vector
Give the rule for the translation
shown
(Pre-image is dashed)
Translate Point H according to
the mapping DM
A B
C
D
F
G
H
I
K
L
M
P
Q
R
S
U
V
X
Y
E
J
N O
T
Z
RULE: (x, y)(x-3, y+2)
Translate according to the
given vector
Give the rule for the translation
shown
(Pre-image is dashed)
Translate Point B according to
the mapping HT
A B
C
D
F
G
H
I
K
L
M
P
Q
R
S
U
V
X
Y
E
J
N O
T
Z
70
Rotations
1) Figures are rotated about the _________________ a certain number of degrees.
2) Positive rotations go _______________________. Example ______________
3) Negative rotations go _______________________. Example ______________
Given that each space between the lines represents 15⁰, answer the following:
4) Rotate A 30⁰, Rotate B 90⁰
5) Rotate C -120⁰, Rotate D -75⁰
D
A
O
o
O
o
B
C
Rotate the following:
6) Rotate E 180⁰, Rotate F -90⁰
7) Rotate G -270⁰, Rotate H 90⁰
G
H
E
F
8) What would a rotation of 360⁰ do? __________________________
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Rotations
Name ________________
Warm -up Review
1) Reflect over x-axis
2) Reflect over y-axis
2
1
3) Translate <-5, -4>
3
Notes:
 Rotations are ______________
 The point about which it is rotated is called the ___________________
 90 degrees= _______________________
 180 degrees= ______________________
 270 degrees = three-quarters of a turn
 Rotate objects _________________ if the degree measurement is positive
 Rotate ______________________ if the degrees are negative
 The is a special coordinate plane used in rotations called a _____________ plane
EXAMPLE: Rotate the triangle 60 degrees about point O:
O






In this polar coordinate plane, each point will stay on the same circle and will
just move a certain number of jumps around the circle
Each “jump” in the polar plane = _____________ degrees
Rotating 60 degrees = _________________ counterclockwise
Rotating -45 degrees = 3 jumps __________________
Rotating 135 degrees = ______________ jumps counterclockwise
Sometimes it is easier to go backwards! 330 degrees would be 22 (330/15)
jumps counterclockwise or ______________________________
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Other Examples:
1. Rotate AB 900 about point O.
2. Rotate AB 1800 about point O
B
A
O
A
B
3.
O
Find the angle of rotation.
4. Find the angle of rotation.
PreImage
Image
P
PreImage
Image
P
5. Rotate AB about point K 135 degrees
6. Rotate ABC 120 degrees:
What angle of rotation maps CKD onto HKG?
A
B
A
B
C
H
C
O
K
D
G
F
E
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Rotations
Name ___________________
Date _____________ Period _____
Rotate the following figures according to the degree indicated. Label your points using mapping
notation.
1. 45°
2. 120°
O
3. 300°
O
O
O O
4. -90°
O
7. 15°
5. -210°
6. -105°
O
O
8. 75°
9. 165°
O
O
O
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Find the angle of rotation about O from preimage (bolded) to the image (dotted) for the following.
10.
11.
12.
O
O
O
13. Rotate AB 90° about point O.
14. Rotate AB 180° about point O.
A
O
O
O
A
B
B
Perform the indicated rotation according to the degrees given using patty paper or a protractor.
15. 90°
about point P
16. 180° about point Q
17. 270° about point R
P
Q
R
Find the mapped point from the given point and
angle of rotation about point O.
18.
19.
20.
21.
22.
Point B rotated 120° is point ________
Point E rotated 60° is point _________
CD rotated 300° is _______________
FOA rotated 240° is _____________
DE rotated –120° is ______________
A
F
E
B
O
D
C
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Name_____________________
Translation Activity
Date ____________Period ______
Warm up Review:
1.Reflect over x-axis
2. Rotate 180⁰
3. Translate <x+4,y+ 3> 4. Reflect over x-axis
Activity:
5. Reflect the figure over k then m.
k
6. Reflect the figure over k then m.
k
m
m
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Special Transformations
Define the following:
Glide Reflection
Composition
Transformation
Isometry
Complete each Transformation:
1. Reflect each point over the
x-axis then the y-axis.
2. Reflect the figure over the x-axis
then the line x = -1.
Y
Z
3. Complete the following pattern of footprints using glide reflections.
77
Compositions Reflections Homework
Name __________________
Date _______Period ______
For 1 and 2, reflect the figure over k then m.
1. 2.
k
m
k
m
For 3 and 4, reflect the figure over K then m.
3.
k
4.
k
m
m
For 5, reflect over k, m then o.
5.
k
m
o
6. Using problem #1, what transformation results from the preimage to the image?
7. Using problem #3, what transformation results from the preimage to the image?
8. Using problem #5, what transformation results from the preimage to the image?
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For 9 and 10, reflect each figure over the x-axis and then over the y-axis.
9.
10.
M
L
F
N
U
11. Reflect the figure over the y-axis
and then over the line y = -x.
12. Reflect the figure over the x-axis
and then over the line y = x.
A
E
D
13. Draw a glide reflection using the
translation <x+0, y-4> and the line of
reflection x = 1.
A
14. Draw a glide reflection using
the translation <x-3, y=0> and the line of
reflection y = - 1.
A
C
B
B
T
O
A
79