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Chapter 1. Unit 1: Transformations, Congruence and Similarity
1.3 Graphs of Translations
Here you will learn how to graph a translation given a description of the translation.
Triangle ABC has coordinates A(1, 1), B(8, 1) and C(5, 8). Draw the triangle on the Cartesian plane. Translate the
triangle up 4 units and over 2 units to the right. State the coordinates of the resulting image.
Watch This
First watch this video to learn about graphs of translations.
MEDIA
Click image to the left for more content.
CK-12 FoundationChapter10GraphsofTranslationsA
Then watch this video to see some examples.
MEDIA
Click image to the left for more content.
CK-12 FoundationChapter10GraphsofTranslationsB
Guidance
In geometry, a transformation is an operation that moves, flips, or changes a shape (called the preimage) to create a
new shape (called the image). A translation is a type of transformation that moves each point in a figure the same
distance in the same direction. Translations are often referred to as slides. When you perform a translation on a
shape, the coordinates of that shape will change:
• translating up means you will add the translated unit to the y coordinate of the (x, y) points in the preimage
• translating down means you will subtract the translated unit from the y coordinate of the (x, y) points in the
preimage
• translating right means you will add the translated unit to the x coordinate of the (x, y) points in the preimage
• translating left means you will subtract the translated unit from the x coordinate of the (x, y) points in the
preimage
Example A
Line AB drawn from (-4, 2) to (3, 2) has been translated 3 units down and 7 units to the left. Draw the preimage and
image and properly label each.
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1.3. Graphs of Translations
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Solution:
Example B
Triangle A is translated 3 units up and 5 units to the right to make triangle B. Find the coordinates of triangle B. On
the diagram, draw and label triangle B.
Solution:
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Chapter 1. Unit 1: Transformations, Congruence and Similarity
Example C
The following figure is translated 4 units down and 6 units to the left to make a translated image. Find the coordinates
of the translated image. On the diagram, draw and label the image.
Solution:
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1.3. Graphs of Translations
Concept Problem Revisited
The coordinates of the new image are A (5, 3), B (12, 3) and C (9, 10).
Vocabulary
Image
In a transformation, the final figure is called the image.
Preimage
In a transformation, the original figure is called the preimage.
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Chapter 1. Unit 1: Transformations, Congruence and Similarity
Transformation
A transformation is an operation that is performed on a shape that moves or changes it in some way. There
are four types of transformations: translations, reflections, dilations and rotations.
Translation
A translation is an example of a transformation that moves each point of a shape the same distance and in the
same direction. Translations are also known as slides.
Guided Practice
1. Line ST drawn from (-3, -3) to (-3, 8) has been translated 4 units up and 3 units to the right. Draw the preimage
and image and properly label each.
2. The polygon below has been translated 3 units down and 10 units to the right. Draw the translated image and
properly label each.
3. The purple pentagon is translated 5 units up and 8 units to the right to make the translated pentagon. Find the
coordinates of the purple pentagon. On the diagram, draw and label the translated pentagon.
Answers:
1.
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1.3. Graphs of Translations
2.
3.
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Chapter 1. Unit 1: Transformations, Congruence and Similarity
Practice
1. Translate the above figure 3 units to the right and 4 units down.
2. Translate the above figure 2 units to the left and 2 units up.
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1.3. Graphs of Translations
3. Translate the above figure 3 units to the right and 2 units down.
4. Translate the above figure 5 units to the left and 1 unit up.
5. Translate the above figure 2 units to the right and 3 units down.
6. Translate the above figure 4 units to the left and 1 unit up.
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Chapter 1. Unit 1: Transformations, Congruence and Similarity
7. Translate the above figure 6 units to the right and 2 units down.
8. Translate the above figure 4 units to the left and 6 units up.
9. Translate the above figure 2 units to the right and 3 units down.
10. Translate the above figure 5 units to the left and 5 units up.
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1.3. Graphs of Translations
11. Translate the above figure 3 units to the right and 6 units down.
12. Translate the above figure 2 units to the left and 2 units up.
13. Translate the above figure 3 units to the right and 3 units down.
14. Translate the above figure 5 units to the left and 2 units up.
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Chapter 1. Unit 1: Transformations, Congruence and Similarity
15. Translate the above figure 7 units to the right and 4 units down.
16. Translate the above figure 1 unit to the left and 2 units up.
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