This document contains notes from a geometry lesson on translations. It defines a translation as moving all points of a figure the same distance in the same direction. It provides examples of translating figures along vectors and describes translations using words like up, down, left and right. It lists the properties of translations that are preserved, like distance, angle measures, parallelism and collinearity. The lesson explains how to translate figures on the coordinate plane by listing the pre-image and image points. Students practice describing translations and explaining the procedure to translate a figure on the coordinate plane.

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Module 8.2 Lesson 3
Day 1
Translating Lines
Do Now:
Supplemental Practice
pg 20-22
Explain your procedure
for translating a figure
along a vector.

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What is a translation?
Is this a translation?

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A translation is a transformation where all the
points of a figure are moved the same distance in
the same direction.
A translation is an isometry, so the image is
congruent to the pre-image.
Is a translation isometric?
pg 13

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Is this a translation?

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A
B
C
A'
B'
C'
A
B
C
B'
C'
A'
A
B
C
A'
B'
C'
A
B
C
A'
C'
B'
T
Which are examples of TRANSLATIONS?
Clone
T T

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There are 4 ways a translation can be seen
1. Using a Vector (on & off the coordinate plane)
ex) Translate Pt P along vector AB
2. Description Translation
ex) Translate 2 units to the right and 3 units down.
3. Mapping Translation
ex) (x,y) (x+2, y-7)
4. Notation Translation
ex) T(2,-3)
pg 13

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Turn to page
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Properties of Translations
1. Distance (lengths of segments are the same)
2. Angle measures (remain the same)
3. Parallelism (parallel lines remain parallel)
4. Colinearity (points stay on the same lines)
5. Midpoint (midpoints remain the same in each figure)
6. Orientation (lettering order remains the same)
Write this
down!
Write this
down!
Bottom of page 13

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Let us quick review the coordinate plane

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Translate triangle ABC along vector XY
A
B C
X
Y
7.
List points:
Pre-image Image
A( , )
B( , )
C( , )
A'( , )
B'( , )
C'( , )
A
B C
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Translate triangle ABC along vector XY
A
B C
X
Y
7.
List points:
Pre-image Image
A(-4, 3)
B(-5, 1)
C(-3, 1)
A'(-1, 4)
B'(-2, 2)
C'(0, 2)
A
B C
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Translate triangle ABC along vector XYA
B C
X
Y
8.
List points:
Pre-image Image
A( , )
B( , )
C( , )
A'( , )
B'( , )
C'( , )
A
B C
17

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Translate triangle ABC along vector XYA
B C
X
Y
8.
List points:
Pre-image Image
A(4, 6)
B(3, 4)
C(5, 4)
A'(6, 3)
B'(5, 1)
C'(7, 1)
A
B C
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EVERY POINT on the figure
undergoes the SAME transformation
Description = a verbal expression
Describe each translation using words like
units, up, down, left, and right.

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Let's Try!
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Let's Try!
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Describe this Translation
A
B
C
A'
B'
C'
ABC A'B'C'3.
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ABC A'B'C'Describe the
Translation!
A
B
C
A'
B'
C'
4.
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Closing Activity:
Explain your procedure for translating a figure
on the coordinate plane.

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