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8th Grade
2D Geometry: Transformations
20161024

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Table of Contents
•
Reflections
•
Dilations
•
Translations
Click on a topic to
go to that section
•
Rotations
•
Transformations
•
Congruence & Similarity
•
Special Pairs of Angles
•
Symmetry
•
Glossary
•
Remote Exterior Angles
TeacherNotes

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Transformations
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Table of
Contents

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Any time you move, shrink, or enlarge a figure you make a
transformation
.
A
B
C
A'
B'
C'
preimage
image
Transformation
TeacherNotes
If the figure you are moving (
preimage
) is labeled
with letters A, B, and C, you can label the points on the
transformed figure (
image
) with the same letters and the prime
sign.

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The image can also be labeled with new letters as shown below.
Triangle
ABC
is the preimage to the reflected image triangle XYZ
A
B
C
X
Y
Z
preimage
image
Transformation

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There are four types of transformations in this unit:
•
Translations
•
Rotations
•
Reflections
•
Dilations
Transformations
The first three transformations preserve the size and shape of the
figure. Therefore, both the preimage and image will be
congruent
.
Congruent figures are same size and same shape.
In other words:
If your preimage is a trapezoid, your image is a congruent
trapezoid.
If your preimage is an angle, your image is an angle with the same
measure.
If your preimage contains parallel lines, your image contains
parallel lines.

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Translations
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Table of
Contents

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Translations

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A
translation
is a slide that moves a figure to a different
position (left, right, up or down) without changing its
size or shape and without flipping or turning it.
Translation
You can use a slide arrow to
show the direction and distance
of the movement.

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This shows a translation of preimage ABC to image
A'B'C'. Each point in the preimage was moved
right 7 and up 4.
Translation

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Click for web page
Translation

Are the line segments in the preimage and image the same
length? In other words, was the size of the figure preserved?
A
B
C
D
A'
B'
C'
D'
To complete a translation, move each point of the preimage and
label the new point.
Example: Move the figure left 2 units and up 5 units.
What are the coordinates of the preimage and image?
Answer

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click to reveal

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Translate preimage ABC 2 left and 6 down.
What are the coordinates of the image and preimage?
A
B
C