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Graphs of Translations

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Graphs and Rules for Translations
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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.

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