You are viewing an older version of this Study Guide. Go to the latest version.

# Graphs of Translations

## Graph images given preimage and translation

%
Progress

MEMORY METER
This indicates how strong in your memory this concept is
Progress
%
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 \begin{align*}y\end{align*} coordinate of the \begin{align*}(x, y)\end{align*}points in the preimage
• translating ______ means you will subtract the translated unit from the \begin{align*}y\end{align*} coordinate of the\begin{align*}(x, y)\end{align*} points in the preimage
• translating ______ means you will add the translated unit to the \begin{align*}x\end{align*} coordinate of the \begin{align*}(x, y)\end{align*}points in the preimage
• translating ______ means you will subtract the translated unit from the \begin{align*}x\end{align*} coordinate of the\begin{align*}(x, y)\end{align*} points in the preimage

.

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

.

#### 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 \begin{align*}T_{(3, \ 5)}\end{align*} . This notation tells you to add 3 to the \begin{align*}x\end{align*} values and add 5 to the \begin{align*}y\end{align*} values.
2. The second notation is a mapping rule of the form \begin{align*}(x, y) \rightarrow (x-7, y+5)\end{align*} . This notation tells you that the \begin{align*}x\end{align*} and \begin{align*}y\end{align*} coordinates are translated to \begin{align*}x - 7\end{align*} and \begin{align*}y + 5\end{align*} .
Which notation is the most common? ____________________
.
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.
.
Write the mapping rule to describe the movement of the points in each of the translations below.
1. \begin{align*}B(-4, -2) \rightarrow B^\prime(2, -2)\end{align*}
2. \begin{align*}A(2, 4) \rightarrow A^\prime(2, 6)\end{align*}
3. \begin{align*}C(-5, -3) \rightarrow C^\prime (-3, 4)\end{align*}

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