Transformations



Transformations A Dilation

Math 512 – Montclair State University With the TI-84

Spring, 2007

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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 2 - 3

Solutions and Notes 4

Expected Outcomes

Students will

▪ Develop a plot

▪ Graph it

▪ Dilate the graph

▪ Measure lengths and angles

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NCTM Standards 2000

Algebra Representation

Geometry Communication

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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

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)

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 pre-image?

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 pre-image?

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

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).

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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.

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:

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