Video solutions to help Grade 8 students learn how to perform translations of figures along a specific vector.

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Lessons for Grade 8

Common Core For Grade 8

• Students perform translations of figures along a specific vector. Students label the image of the figure using
appropriate notation.

• Students learn that a translation maps lines to lines, rays to rays, segments to segments, and angles to angles.
Students learn that translations preserve lengths of segments and degrees of angles.

Lesson 2 Summary

Translation occurs along a given vector:

• A vector is a segment in the plane. One of its two endpoints is known as a starting point; while the
other is known simply as the endpoint.

• The length of a vector is, by definition, the length of its underlying segment.

• Pictorially note the starting and endpoints:

A translation of a plane along a given vector is a basic rigid motion of a plane.

The three basic properties of translation are:

(T1) A translation maps a line to a line, a ray to a ray, a segment to a segment, and an angle to an angle.

(T2) A translation preserves lengths of segments.

(T3) A translation preserves degrees of angles.

Classwork

Discussion

• What is the simplest transformation that would map one of the following figures to the other?

Example 1

• A vector is a segment in the plane. One of its two endpoints is designated as a starting point; while the other is
simply called the endpoint.

Example 2

We are going to describe how to define a
translation along a vector AB by the use of an
overhead projector transparency.

Exercise 1

Draw at least three different vectors and show what a translation of the plane along each vector will look like. Describe
what happens to the following figures under each translation, using appropriate vocabulary and notation as needed.

Exercise 2

The diagram below shows figures and their images under a translation along HI. Use the original figures and the
translated images to fill in missing labels for points and measures.