Transformations
A Dilation
Math 512 – Montclair State University
Spring, 2007
With the TI-84
Description
In this activity students will review:
1. The StatPlot menu of the TI-84
2. Entering lists.
3. A transformation – a dilation (scale factor)
4. Measure lengths and angles
Contents
Pages
Student worksheet
Solutions and Notes
2-3
4
Expected Outcomes
Students will

Develop a plot

Graph it

Dilate the graph

Measure lengths and angles
NCTM Standards 2000
Algebra
Geometry
Representation
Communication
2
Worksheet 1
Using the TI-84 to draw a triangle:
1. Turn on your calculator.
2. Clear the y= editor.
3. Press STAT
4. Highlight 1:Edit
5. Press ENTER
6. In L1 enter the x values of the triangles ordered pairs (You should enter 2,2,4,2)
(Why are four values needed?)
7. In L2 enter the y values of the triangles ordered pairs. You should enter 4,2,2,4)
(Why are four values needed?)
8. Press 2nd StatPlot
9. Highlight 1:Plot 1 and ENTER
10. Mover the blinking cursor until it flashes over the On, press ENTER
11. Move the cursor to Type and highlight the second choice, press ENTER
12. Check to see that Xlist is L1 and Ylist is L2 (if not change them)
13. Move to Mark and highlight the . and press ENTER
14. Press Graph
You should see the graph of your triangle.
15. Change the viewing window: Press window
16. Change Xmin to 0 and Ymin to 0
17. Press Graph
3
Using the TI – 84 to dilate the triangle:
1. Press Stat
2. Highlight 1:Edit and press ENTER
3. Move the cursor to L3 so that it is highlighted
4. Press 2nd L1 * 2 and ENTER (a list of values appears in L3)
5. Highlight L4 and press 2nd L2 * 2 and ENTER
6. Press 2nd StatPlot
7. Highlight 2:plot 2 and press ENTER
8. Highlight ON and press ENTER
9. Choose Type: the second one
10. Move to Xlist and Press 2nd L3 and Ylist press 2nd L4
11. Move to the mark and choose the . and press ENTER
12. 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:
1.
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)
4
2.
Below is the image and pre-image labeled. This will help when you record the
values.
D
A
B
C
E
F
3.
What is the length of the side DE of the image? The length of AB of the preimage?
4.
Repeat this process for the remaining sides of both the image and pre-image.
Side BC=
Side EF=
5.
How can we find the length of sides AC and DF? What are the lengths?
6.
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 preimage?
7.
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
5
Worksheet 2
1. 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
2. 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
1. Distribute graph paper. Have each student draw their own picture and determine
the points needed to create the picture as a scatter plot.
2. Have pairs of students exchange papers and create the scatter plot to see the
picture their partner created.
6
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:
7
The screen for the graph of the dilation should
look like:
Dilation by a factor of ¼ should look like: