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Course: 8th grade (Illustrative Mathematics) > Unit 1

Lesson 2: Lesson 5: Coordinate moves
Math
8th grade (Illustrative Mathematics)
Rigid transformations and congruence
Lesson 5: Coordinate moves
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Translations review

Google Classroom
Review the basics of translations, and then perform some translations.

What is a translation?

A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.
This translation maps △XYZ onto the blue triangle.
A coordinate plane with a triangle having vertices X at (negative 9, 6), Y at (2,3), and Z at (negative 2, negative 8). The x and y axes scale by one. The triangle is shifted 3 units to the right to form a new triangle. The vertex that corresponds with X is (negative 6, 6). The vertex that corresponds with Y is (5, 3). The vertex that corresponds with Z is (1, negative 8).
The result is a new figure, called the image. The image is congruent to the original figure.
Want to learn more about different types of transformations? Check out this video.

Performing translations

A figure can be moved horizontally along the x axis and vertically along the y axis.
Example:
Translate △LMN −4 units in the x direction and −2 units in the y direction.
A translation of −4 units in the x direction results in a shift to the left by 4 units, and a translation of −2 units in the y direction results in a shift down by 2 units.
A coordinate plane with a triangle having vertices L at (negative 3, negative 2), M at (negative 5, negative 2), and N at (negative 2, 3). The x and y-axes scale by one. A dashed line moves 4 units left and 2 units down from all three vertices to show the corresponding vertices of a new triangle with vertices at (negative 7, negative 4), (negative 9, negative 4), and (negative 6, 1).
This translation maps △LMN onto the triangle below.
A coordinate plane with a triangle having vertices L at (negative 3, negative 2), M at (negative 5, negative 2), and N at (negative 2, 3). The x and y axes scale by one. The triangle is shifted 4 units to the left and 2 units down to form a new triangle. The vertex that corresponds with L is (negative 7, negative 4). The vertex that corresponds with M is (negative 9, negative 4). The vertex that corresponds with N is (negative 6, 1).
Want to learn more about performing translations? Check out this video.

Practice

Problem 1
Draw the image of △ABC under a translation by 3 units to the right and 4 units down.

Want to try more problems like this? Check out this exercise.

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