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# 13.1: Translations with Lists

Difficulty Level: At Grade Created by: CK-12

This activity is intended to supplement Geometry, Chapter 12, Lessons 2 and 3.

## Problem 1 – Creating a Scatter Plot

Open the list editor by pressing STAT ENTER. Enter the x\begin{align*}x-\end{align*}values into list L1\begin{align*}L_1\end{align*} and the y\begin{align*}y-\end{align*}values into list L2\begin{align*}L_2\end{align*}.

xy23838112589872723\begin{align*}x && 2 && 8 && 8 && 12 && 8 && 8 && 2 && 2\\ y && 3 && 3 && 1 && 5 && 9 && 7 && 7 && 3\end{align*}

Create a connected scatter plot of L1\begin{align*}L_1\end{align*} vs. L2\begin{align*}L_2\end{align*}.

Press 2nd [Y=]\begin{align*}2^{nd} \ [Y=]\end{align*} and select Plot1. Change the settings to match those shown at the right.

Press WINDOW and adjust the window settings to those shown at the right.

Press GRAPH to view the scatter plot.

Sketch the scatter plot.

## Problem 2 – Reflections and Rotations

Go back to the list editor. Enter the formula =L1\begin{align*}= -L_1\end{align*} at the top of list L3\begin{align*}L_3\end{align*} to create the opposite of each of the x\begin{align*}x-\end{align*}values in L1\begin{align*}L_1\end{align*}.

Then, enter the formula =L2\begin{align*}= -L_2\end{align*} at the top of list L4\begin{align*}L_4\end{align*} to create the opposite of each of the y\begin{align*}y-\end{align*}values in L2\begin{align*}L_2\end{align*}.

Graph the following scatter plots using Plot2, one at a time. For each combination of lists, determine what type of reflection occurred.

Press GRAPH to view Plot1 and Plot2 together.

A: xL3\begin{align*}x \leftarrow L_3\end{align*} and yL2\begin{align*}y \leftarrow L_2\end{align*}

(x,y)\begin{align*}(-x, y)\end{align*} ________

B: xL1\begin{align*}x \leftarrow L_1\end{align*} and yL4\begin{align*}y \leftarrow L_4\end{align*}

(x,y)\begin{align*}(x, -y)\end{align*} ________

C: xL2\begin{align*}x \leftarrow L_2\end{align*} and yL1\begin{align*}y \leftarrow L_1\end{align*}

(y,x)\begin{align*}(y, x)\end{align*} ________

Use Plot2 to create the following scatter plots. For each combination, determine what type of rotation occurred.

D: xL4\begin{align*}x \leftarrow L_4\end{align*} and yL1\begin{align*}y \leftarrow L_1\end{align*}

(y,x)\begin{align*}(-y, x)\end{align*} ________

E: xL2\begin{align*}x \leftarrow L_2\end{align*} and yL3\begin{align*}y \leftarrow L_3\end{align*}

(x,y)\begin{align*}(-x, -y)\end{align*} ________

F: xL3\begin{align*}x \leftarrow L_3\end{align*} and yL4\begin{align*}y \leftarrow L_4\end{align*}

(y,x)\begin{align*}(y, -x)\end{align*} ________

## Problem 3 – Translations

Press STAT ENTER to go back to the list editor.

In the formula bar for L3, enter=L15\begin{align*}L_3,\ \text{enter} = L_1-5\end{align*} to translate the x\begin{align*}x-\end{align*}values. In the formula bar for L4, enter=L2+3\begin{align*}L_4, \ \text{enter} = L_2+3\end{align*} to translate the y\begin{align*}y-\end{align*}values.

Change Plot2 so that the Xlist is L3\begin{align*}L_3\end{align*} and the Ylist is L4\begin{align*}L_4\end{align*}. Press GRAPH to view the scatter plots.

Where did the image shift? How many units left/right and how many units up/down?

Translate the scatter plot into Quadrant 3 by editing the formula bars for L3\begin{align*}L_3\end{align*} and L4\begin{align*}L_4\end{align*}.

L3\begin{align*}L_3\end{align*} formula: _____________

L4\begin{align*}L_4\end{align*} formula: _____________

Explain how the image shifted.

## Problem 4 – Dilations

In the list editor, change the formula for L3\begin{align*}L_3\end{align*} to =0.5L1\begin{align*}= 0.5^*L_1\end{align*} and the formula for L4\begin{align*}L_4\end{align*} to =0.5L2\begin{align*}= 0.5^*L_2\end{align*}.

Press GRAPH to view the scatter plots.

Explain what happened to the image.

Dilate the scatter plot into Quadrant 3 by editing the formula bars for L3\begin{align*}L_3\end{align*} and L4\begin{align*}L_4\end{align*}.

\begin{align*}L_3\end{align*} formula: _____________

\begin{align*}L_4\end{align*} formula: _____________

Explain what happened to the image.

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