Topics
8. Transformations & Congruence
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United States of America
Grade 8

8.01 Properties of translations

Lesson
Practice

Introduction

This lesson introduces transformation of an object or shape on a coordinate plane by translation. Transformation means change. We will learn how to describe the translation of an object based on the direction of movement.

Translations

A translation is what occurs when we move an object or shape from one place to another without changing its size, shape or orientation. Sometimes called a slide, a translation moves every point on an object or shape the same distance in the same direction.

To identify and describe a translation

  1. Look for corresponding points on the object

  2. Identify if the object has moved horizontally or vertically, and then describe that movement as left/right or up/down

  3. Count the number of places (or units) that the object has moved

Exploration

This applet shows the translation of an object to its image. You can use the sliders to change the horizontal and vertical amounts.

Loading interactive...

When an object is being translated, its image moves without changing size or shape, rotating or reflecting.

Examples

Example 1

What is the translation from triangle ABC to triangle A'B'C'?

-2
2
4
6
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10
x
-6
-4
-2
2
4
6
y
A
4 units down
B
4 units up
C
7 units down
D
7 units up
Worked Solution
Create a strategy

Consider just one vertex from triangle ABC and the corresponding vertex from triangle A'B'C'. Count the units between each vertex and consider the direction of movement.

Apply the idea

Consider vertices C and C'. We count 7 units up from C to C'.

-2
2
4
6
8
10
x
-6
-4
-2
2
4
6
y

So the answer is Option D.

Example 2

What is the translation from quadrilateral A to quadrilateral B?

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2
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9
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x
1
2
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7
8
y
A
2 units left and 4 units down
B
4 units left and 2 units down
C
4 units right and 2 units up
D
2 units right and 4 units up
Worked Solution
Create a strategy

Identify the directions of the movements of the corresponding vertices and count the number of steps.

Apply the idea

We can see that the vertices moved 4 units right and 2 units up.

1
2
3
4
5
6
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8
9
10
x
1
2
3
4
5
6
7
8
y

So the answer is option C.

Idea summary

To identify and describe a translation

  1. Look for corresponding points on the object

  2. Identify if the object has moved horizontally or vertically, and then describe that movement as left/right or up/down

  3. Count the number of places (or units) that the object has moved

Outcomes

8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations.

8.G.A.1.A

Lines are taken to lines, and line segments to line segments of the same length.

8.G.A.1.B

Angles are taken to angles of the same measure.

8.G.A.1.C

Parallel lines are taken to parallel lines.

8.G.A.3

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

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