This activity is intended to supplement Geometry, Chapter 12, Lessons 2 and 3.
Time required: 40 minutes
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 the y−values of the figure.
To perform a dilation, multiply a constant scale factor by the list with the x−values or the y−values of the figure.
This activity is designed to be student-centered 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.
Problem 1 – Creating a Scatter Plot
Problem 2 – Reflections and Rotations
For each combination of lists, students are to determine what type of reflection occurred.
Use Plot2 to create the following scatter plots. For each combination, determine what type of rotation occurred.
Problem 3 – Translations
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.
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.
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.