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Wize High School Geometry Textbook (Common Core) > Transformations of Shapes in 2D

Translations

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Translations



There are many things we can do to an object that preserves its properties, or allows it to have similar properties. A translation is one of these.

Translations

A translation moves every point of an object to a new location. This is done in the same direction and at the same distance away.

A translation is a type of transformation. A transformation is a function that changes or moves an object to produce a new one.

Properties of Translations

  • Translation postulate - A translated segment or angle will have the same length or measure as the original.
  • Composition postulate - Translating an object using two translations can be done using a single translation.

Example
  1. Translate the given rectangle by moving it right 3 units and then up 4 units.
  2. Show that this is the same as moving it diagonally 5 units.

ANSWER:

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Working with Translations



While working on a report your friend decided to make two copies. These two copies, along with the original were then set on a table.


Use the diagram of the situation, and the fact that the original is labeled AA, to answer the questions.

1. Of these two copies, which one can be considered a translation of the original?

ANSWER: The copy labeled as BB is a translation of the original. All of the points have been moved in the same direction, and the same distance. The copy labeled as CC appears to be translated, and rotated.

2. If the long side of the original was 11 inches, what is the length of the long side of the translated copy?

ANSWER: Because corresponding sides of a translated copy will be the same length, we can conclude that the long side of the copy will also be 11 inches.

3. If all of the original angles were right angles, what are the angles of the translated copy?

ANSWER: Because corresponding angles of a translated copy will be the same measure, we can conclude that all of the angles will also be right angles, or 90 degrees.

Identify the translation



Here are several different transformations of a triangle.
Which one of them is considered a translation?

Translations and Algebra



While working planting a pasture, famer Jones decides to make a field that is a translation of an existing field.
Use the diagram of this translation to answer the questions.


1. What is the value of xx?
2. What is the value of yy?
3. What is the value of ww?
1. What is the value of xx?

Translations and Fishing



While fishing, Elsa starts at point AA, and finds that her boat as slowly moved to point BBas seen in the diagram. Use the given information to answer the questions.


1. If each square in the diagram represents 5 kilometers, how far did she travel?

2. Her movement can be seen as two translations. What is the best description of these translations?
1. If each square in the diagram represents 5 kilometers, how far did she travel? (Round your answer to the nearest km)