# Translation and Properties

Related Topics:
Lesson Plans and Worksheets for Grade 8
Lesson Plans and Worksheets for all Grades

Videos, examples, and 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

Worksheets and solutions for Common Core Grade 8, Module 2, 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.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.