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13.1: Translations with Lists

Difficulty Level: At Grade Created by: CK-12
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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 \begin{align*}x-\end{align*}xvalues into list \begin{align*}L_1\end{align*}L1 and the \begin{align*}y-\end{align*}yvalues into list \begin{align*}L_2\end{align*}L2.

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

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

Press \begin{align*}2^{nd} \ [Y=]\end{align*}2nd [Y=] 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 \begin{align*}= -L_1\end{align*}=L1 at the top of list \begin{align*}L_3\end{align*}L3 to create the opposite of each of the \begin{align*}x-\end{align*}xvalues in \begin{align*}L_1\end{align*}L1.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Problem 3 – Translations

Press STAT ENTER to go back to the list editor.

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

Change Plot2 so that the Xlist is \begin{align*}L_3\end{align*} and the Ylist is \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 \begin{align*}L_3\end{align*} and \begin{align*}L_4\end{align*}.

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

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

Explain how the image shifted.

Problem 4 – Dilations

In the list editor, change the formula for \begin{align*}L_3\end{align*} to \begin{align*}= 0.5^*L_1\end{align*} and the formula for \begin{align*}L_4\end{align*} to \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 \begin{align*}L_3\end{align*} and \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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