Geometry Translations Explained

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When you take a figure and move it along a straight line without twisting or turning it, this is called translation.

Translated phone

This mobile phone has been translated, because it has been slid along, but not been twisted or turned.

When you need to translate a figure, you draw the figure in the exact same way somewhere else on your paper. It’s extremely important to not twist or turn the figure.

Example 1

Translating this bicycle $4$ cm to the right looks like this:

A moving bike is being translated

This monkey has been translated, because it has not been twisted or turned during its fall.

Three trees and monkeys

Think About This

What if the monkey was sitting on a swing? Would the movement still be a translation?

The answer is no. When the monkey sits on the swing, it’s moving in an arc, not along a straight line. Curved movement like this is called rotation. In this case, the monkey is rotating about the point where the swing is attached to the frame. See the picture below.

A monkey on a swing is rotated, not translated

This monkey has not been translated, it has been rotated.

When translating an object, you need to move all the points the same distance in the same direction. Translating something basically means moving an object in a straight line without rotating it.

Rule

Instructions for Translations

1.: Name all the vertices. Use letters; first $A$ , then $B$ , $C$ , etc.
2.: Put your ruler through point $A$ , measure $a$ inches to the right/left, and mark a point.
3.: Now you measure $b$ inches down/up from the point you just made. Make a new point and call it $A^{'}$ .
4.: Repeat for all vertices.
5.: Connect the points $A^{'}$ , $B^{'}$ , $C^{'}$ , etc. with line segments.

Think About This

A curious thought: When you walk down the sidewalk in a straight line, you translate yourself. You also translate yourself when skiing down a hill. There are many fun things in your everyday life that are translations.

Triangle translated 2 to the right and 3 down

This triangle has been translated 2 to the right and 3 down.

Circle translated 3 to the left and 4 up

This circle has been translated 3 to the left and 4 up.

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