Dismiss
Skip Navigation

12.2: Translations

Difficulty Level: At Grade Created by: CK-12
Turn In

Learning Objectives

  • Graph a point, line, or figure and translate it and units.
  • Write a translation rule.

Review Queue

  1. Find the equation of the line that contains (9, -1) and (5, 7).
  2. What type of quadrilateral is formed by and ?
  3. Find the equation of the line parallel to #1 that passes through (4, -3).

Know What? The distances between San Francisco, , Paso Robles, , and Ukiah, , are given in miles the graph. Find:

a) The translation rule for to .

b) The translation rule for to .

c) The translation rule for to .

d) The translation rule for to . It is not the same as part b.

Transformations

Transformation: An operation that moves, flips, or changes a figure to create a new figure.

Rigid Transformation: A transformation that does not change the size or shape of a figure.

The rigid transformations are: translations, reflections, and rotations. The new figure created by a transformation is called the image. The original figure is called the preimage. Another word for a rigid transformation is an isometry or congruence transformations.

In Lesson 7.6, we learned how to label an image. If the preimage is , then the image would be , said “a prime.” If there is an image of , that would be labeled , said “a double prime.”

Translations

Translation: A transformation that moves every point in a figure the same distance in the same direction.

This transformation moves the parallelogram to the right 5 units and up 3 units. It is written .

Example 1: Graph square and . Find the image after the translation . Then, graph and label the image.

Solution: We are going to move the square to the left 2 and up 3.

Example 2: Find the translation rule for to .

Solution: Look at the movement from to . The translation rule is .

Example 3: Show from Example 2.

Solution: Use the distance formula to find all the lengths of the sides of the two triangles.

This verifies our statement at the beginning of the section that a translation is an isometry or congruence translation.

Example 4: Triangle has coordinates and . Translate to the left 4 units and up 5 units. Determine the coordinates of .

Solution: Graph . To translate , subtract 4 from each value and add 5 to each value.

The rule would be .

Know What? Revisited

a)

b)

c)

d)

Review Questions

  • Questions 1-13 are similar to Example 1.
  • Questions 14-17 are similar to Example 2.
  • Questions 18-20 are similar to Example 3.
  • Questions 21-23 are similar to Example 1.
  • Questions 24 and 25 are similar to Example 4.

Use the translation for questions 1-7.

  1. What is the image of ?
  2. What is the image of ?
  3. What is the image of ?
  4. What is the image of ?
  5. What is the preimage of ?
  6. What is the image of ?
  7. Plot and from the questions above. What do you notice?

The vertices of are and . Find the vertices of , given the translation rules below.

In questions 14-17, is the image of . Write the translation rule.

Use the triangles from #17 to answer questions 18-20.

  1. Find the lengths of all the sides of .
  2. Find the lengths of all the sides of .
  3. What can you say about and ? Can you say this for any translation?
  4. If was the preimage and was the image, write the translation rule for #14.
  5. If was the preimage and was the image, write the translation rule for #15.
  6. Find the translation rule that would move to , for #16.
  7. The coordinates of are and . Translate to the right 5 units and up 11 units. Write the translation rule.
  8. The coordinates of quadrilateral are and . Translate to the left 3 units and down 7 units. Write the translation rule.

Review Queue Answers

  1. Kite

Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Show More

Image Attributions

Show Hide Details
Description
Subjects:
Grades:
8 , 9 , 10
Date Created:
Feb 22, 2012
Last Modified:
Aug 15, 2016
Files can only be attached to the latest version of section
Please wait...
Please wait...
Image Detail
Sizes: Medium | Original
 
CK.MAT.ENG.SE.1.Geometry-Basic.12.2