This document contains notes from a math lesson on translations. It defines a translation as a transformation where all points of a figure are moved the same distance in the same direction. Examples of translations are provided, as well as their properties which include preserving distances, angles, parallelism, collinearity and more. Students are given practice problems identifying translations and describing them in words based on vector movements.

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Module 8.2 Lesson 3
Day 1
Translating Lines
HW
Do Now:
Solve the following equation.
(x - 6) = -7
pg 21- 22 # 6-10
CRS #16 due tomorrow
2
3

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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
TT

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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
S.14

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S.15

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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

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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!
S.18

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Let's Try!
S.18

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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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