1
TransformationsA Dilation
Math 512 – Montclair State University With the TI-84
Spring, 2007
Description
In this activity students will review:
- The StatPlot menu of the TI-84
- Entering lists.
- A transformation – a dilation (scale factor)
- Measure lengths and angles
Contents Pages
Student worksheet 2 - 3
Solutions and Notes 4
Expected Outcomes
Students will
- Develop a plot
- Graph it
- Dilate the graph
- Measure lengths and angles
NCTM Standards 2000
AlgebraRepresentation
GeometryCommunication
Worksheet 1
Using the TI-84 to draw a triangle:
- Turn on your calculator.
- Clear the y= editor.
- Press STAT
- Highlight 1:Edit
- Press ENTER
- In L1 enter the x values of the triangles ordered pairs (You should enter 2,2,4,2) (Why are four values needed?)
- In L2 enter the y values of the triangles ordered pairs. You should enter 4,2,2,4) (Why are four values needed?)
- Press 2nd StatPlot
- Highlight 1:Plot 1 and ENTER
- Mover the blinking cursor until it flashes over the On, press ENTER
- Move the cursor to Type and highlight the second choice, press ENTER
- Check to see that Xlist is L1 and Ylist is L2 (if not change them)
- Move to Mark and highlight the . and press ENTER
- Press Graph
You should see the graph of your triangle.
- Change the viewing window: Press window
- Change Xmin to 0 and Ymin to 0
- Press Graph
Using the TI – 84 to dilate the triangle:
- Press Stat
- Highlight 1:Edit and press ENTER
- Move the cursor to L3 so that it is highlighted
- Press 2nd L1 * 2 and ENTER (a list of values appears in L3)
- Highlight L4 and press 2nd L2 * 2 and ENTER
- Press 2nd StatPlot
- Highlight 2:plot 2 and press ENTER
- Highlight ON and press ENTER
- Choose Type: the second one
- Move to Xlist and Press 2nd L3 and Ylist press 2nd L4
- Move to the mark and choose the . and press ENTER
- Press Graph
On your screen you will see the original triangle and a dilation (by a factor of 2) of the original.
Measuring sides and angles of the image and pre-image:
- Your image and pre-image
look like this:
Determine
the length
of this side
Determine
the length
of this side
(Hint: Using the y-axis as a guide count from
endpoint to endpoint of the side)
- Below is the image and pre-image labeled. This will help when you record the values.
D
A
B C E F
- What is the length of the side DE of the image? The length of AB of the pre-image?
- Repeat this process for the remaining sides of both the image and pre-image.
Side BC=
Side EF=
- How can we find the length of sides AC and DF? What are the lengths?
- Compare the lengths of the respective sides of the image and pre-image. What generalization can you make about the lengths of the side of the image and pre-image?
- To test your conjecture, use the directions for creating a dilation but this time multiply L3 and L4 by ¼. Then answer questions 1-6 above again using the new images.
The images will look like:
Pre-image
Image
Worksheet 2
- You can create pictures and dilate those as you did in the exercises in worksheet 1. Enter the values below into L1 and L2 on your calculator.
L1: 4,6,6,7,7,8,8,7,7,4,4,7,10,10,4,4,10
L2: 1,1,3,3,1,1,3,3,1,1,6,8,6,1,1,6,6
- Now create a statplot. Press zoom 9 to see the picture. If you have entered you values correctly you should see a picture of a shed ( see below).
Extension Activity
- Distribute graph paper. Have each student draw their own picture and determine the points needed to create the picture as a scatter plot.
- Have pairs of students exchange papers and create the scatter plot to see the picture their partner created.
Solutions and Teachers Notes
Worksheet 1 – Solution for using the TI – 84 to draw a triangle.
The screen for your lists should look like:
The screen for the StatPlot should look like:
The screen for the graph should look like:
When you change the viewing window,
it should look like:
The StatPlot for Plot 2 should look like:
The screen for the graph of the dilation should
look like:
Dilation by a factor of ¼ should look like: