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# Graphs of Translations

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Graphs and Rules for Translations

### Vocabulary

##### Complete the chart.
 Word Definition Mapping Rule ___________________________________________________________ _____________ the final figure Transformation ___________________________________________________________ Translation ___________________________________________________________ _____________ the original figure

### Graphs of Translations

A translation is a movement of a figure. When you perform a translation on a shape, the coordinates of that shape will change:

• translating ______ means you will add the translated unit to the $y$ coordinate of the $(x, y)$points in the preimage
• translating ______ means you will subtract the translated unit from the $y$ coordinate of the$(x, y)$ points in the preimage
• translating ______ means you will add the translated unit to the $x$ coordinate of the $(x, y)$points in the preimage
• translating ______ means you will subtract the translated unit from the $x$ coordinate of the$(x, y)$ points in the preimage

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Translate the following figures:

1. 2 units down and 3 units right
2. 1 unit up and 5 units left

3. 4 units down and 1 unit left

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#### Rules for Translations

A transformation is an operation that _____________, _____________, or _____________ a shape to create a new shape. There are two notations to write transformations:

1. One notation looks like $T_{(3, \ 5)}$ . This notation tells you to add 3 to the $x$ values and add 5 to the $y$ values.
2. The second notation is a mapping rule of the form $(x, y) \rightarrow (x-7, y+5)$ . This notation tells you that the $x$ and $y$ coordinates are translated to $x - 7$ and $y + 5$ .
Which notation is the most common? ____________________
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A "rule for translation" is just a way of saying how the image was changed. It is the rule to follow if you want to recreate that image.
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Write the mapping rule to describe the movement of the points in each of the translations below.
1. $B(-4, -2) \rightarrow B^\prime(2, -2)$
2. $A(2, 4) \rightarrow A^\prime(2, 6)$
3. $C(-5, -3) \rightarrow C^\prime (-3, 4)$

Write the mapping rule that represents the translation of the preimage to the image for each diagram below.