# Translation and Properties

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

## New York State Common Core Math Module 2, Grade 8, Lesson 2

### Lesson 2 Student Outcomes

• 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.

Have a look at the following animation of translation