13.1: Transformations with Lists
This activity is intended to supplement Geometry, Chapter 12, Lessons 2 and 3.
ID: 10277
Time required: 40 minutes
Activity Overview
Students will graph a figure in the coordinate plane. They will use list operations to perform reflections, rotations, translations and dilations on the figure, and graph the resulting image using a scatter plot.
Topic: Transformational Geometry
 Perform reflections, rotations, translations and dilations using lists and scatter plots to represent figures on a coordinate plane.
Teacher Preparation and Notes
 This activity is designed to be used in a high school geometry or algebra classroom.

If an original point on the coordinate plane is denoted by
(x,y) , then each of the following ordered pairs denotes a transformation:

To perform a translation, add or subtract a constant from the list with the
x− values or they− values of the figure. 
To perform a dilation, multiply a constant scale factor by the list with the
x− values or they− values of the figure.  This activity is designed to be studentcentered with the teacher acting as a facilitator while students work cooperatively. If desired, have students work in groups of 3. Each person in the group should enter a different combination of lists for Problem 2 and the group should discuss the results.
Associated Materials
 Student Worksheet: Translations with Lists http://www.ck12.org/flexr/chapter/9697
Problem 1 – Creating a Scatter Plot
Before beginning the activity, students need to clear all entries from the
First, students will enter the data on the worksheet into lists
After setting up Plot1 for a scatter plot of
Problem 2 – Reflections and Rotations
In the list editor students are to enter the formulas
To type
To type
For each combination of lists, students are to determine what type of reflection occurred.
A:
B:
C:
Use Plot2 to create the following scatter plots. For each combination, determine what type of rotation occurred.
D:
E:
F:
Problem 3 – Translations
In the list editor, students are to enter the formulas
Students should see that the image shifted to the left 5 units and up 3 units. Remind students that the tick marks on the graph are every 2 units.
Now students are to translate the scatter plot into Quadrant 3 by editing the formula bars for
The image shifted 15 units to the left and 10 units down.
Extension – Dilations
Remind students that they have seen dilations in Chapter 7, Lesson 6.
In the list editor, students are to enter the formulas
Students should see that the image decreased in size. If they have trouble seeing the image, they can the mark of the plot to the small dot.
Then students are to 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*}. Remind students that the scale factor needs to be the same for both lists. Possible formulas are below.
\begin{align*}L_3\ \text{formula:} & = 0.5^*L_1\\ L_4\ \text{formula:} & = 0.5^*L_2\end{align*}