Lesson 9-1 - Fort Bend ISD

Name_____________________________________ Class____________________________ Date ________________
Lesson 9-1
Lesson Objectives
1 Identify isometries
2 Find translation images of figures
NAEP 2005 Strand: Geometry
Topic: Transformation of Shapes and Preservation of
Properties; Position and Direction
Translations
Local Standards: ____________________________________
Vocabulary.
A transformation of a geometric figure is
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In a transformation, the preimage is
In a transformation, the image is
An isometry is
A translation (slide) is
A composition of transformations is
Examples.
1
Identifying Isometries Does the transformation appear to be an
isometry
Preimage
Image
The image appears to be the same as the preimage, but .
Because the figures appear to be
, the transformation
appears to be an isometry.
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2
Naming Images and Corresponding Parts In the diagram,
XYZ is an image of ABC.
a. Name the images of B and C.
B
C Z
Y
Because corresponding vertices of the preimage and the
image are listed in the same order, the image of B is ,
and the image of C is .
A
X
b. List all pairs of corresponding sides.
Because corresponding sides of the preimage and the image are
listed in the same order, the following pairs are corresponding sides:
3
AB and , AC and , BC and .
Finding a Translation Image Find the image of ABC
under the translation (x, y) → (x 2, y 3).
A(1, 2) → A( , 3) Use the rule (x, y ) → (x 2, y 3)
B(1, 0) → B( 2, )
C(0, 1) → C( , )
The image of ABC is ABC with A( , ),B( , ),
and C( , ).
Quick Check.
1. Does the transformation appear to be an isometry Explain.
a. b.
Preimage
Preimage Image
2. In the diagram, NID S SUP.
a. Name the images of I and point D.
Image
S
A
C
U
N
y
B
x
P
I
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D
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b. List all pairs of corresponding sides.
3. Find the image of ABC for the translation (x 2, y 1).
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Examples.
4
5
Writing a Rule to Describe a Translation Write a rule to
describe the translation ABC S ABC.
You can use any point on ABC and its image on ABC
to describe the translation. Using A(4, 1) and its image
, the horizontal change is 2 ( ), or ,
and the vertical change is 0 , or .
The rule is (x, y) S
.
Adding Translations Tritt rides his bicycle 3 blocks north and 5 blocks east of a
pharmacy to deliver a prescription. Then he rides 4 blocks south and 8 blocks
west to make a second delivery. How many blocks is he now from the pharmacy
The rule
The rule
west.
Tritt’s position after the second delivery is the
translations.
represents a ride of 3 blocks north and 5 blocks east.
represents a ride of 4 blocks south and 8 blocks
of the two
( , ) translates to ( , ) or ( , ). Then, ( , )
translates to ( , ) or ( , ).
Tritt is block and blocks of the
pharmacy.
A
4
B
4
2
C
2
2
4
y
A
2
B
x
C
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Quick Check.
4. Use the rule (x, y) S (x 7, y 1) to find the translation image of LMN.
Graph the image LMN.
y
6
4
6
L
4
M
2
2
N
2
4
6
2 4 6
x
5. Refer to Example 5. Tritt now makes a third delivery. Starting from where
the second delivery was, he goes 5 blocks north and 1 block west. How
many blocks is Tritt from the pharmacy
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