DON’T WRITE ON THIS PAPER PLEASE
IMAGINE THAT!!!
Directions: Use Geometer’s sketchpad to answer the following questions about transformations. Write your
answers on a separate piece of GRAPH PAPER. Your work will be collected at the end of the class period.
Start by opening the “Imagine That” file in my public folder (cshaw)
Tools to Use in Geometer’s Sketchpad
Selection Tool:
Line Tool:
Point Tool:
For each problem answer the following questions on your graph paper:
a) Label which type of transformation is being performed (translation, reflection, rotation)
b) Draw the transformation that was performed including the original image.
c) Record the coordinates for the new image A’B’C’. How do the coordinates of the new image
compare to the original coordinates?
d) Write a general rule to show how the coordinates will change for all transformations like this
one.
1. Translation:
- Select ABC so that all of the points and segments are highlighted in pink
- Under the “Transform” menu tab select “Translate” (Make sure the “Rectangular translation
vector is selected)
- Enter 2 for the horizontal distance and -3 for the vertical distance. Then click on the “Translate”
button.
- Answer questions a-d on your graph paper
2. Reflection over the x-axis:
- Delete your previous transformation (do not delete the original ABC )
- Select ABC so all of its points and segments are highlighted in pink
- Double click on the x-axis
- Under the “Transform” menu, select “Reflect”
- Answer questions a-d on your graph paper
3. Reflection over the y-axis:
- Delete your previous transformation (do not delete the original ABC )
- Select ABC so all of its points and segments are highlighted
- Double click on the y-axis
- Under the “Transform” menu, select “Reflect”
- Answer questions a-d on your graph paper
4. Reflection over the line y = x
- Delete your previous transformation (do not delete the original ABC )
- Under the “Graph” menu, select “Plot Points”
- Plot a point at (8, 8)
- Using your line tool connect the points (0, 0) and (8, 8)
- Select ABC so the whole thing is highlighted (nothing else can be highlighted!!)
- Double click on the line you just created
- Under the “Transform” menu, select “Reflect”
- Answer questions a-d on your graph paper
5. Reflection over the line y 
1
x3
3
-
Delete everything on your screen except your original triangle, ABC
-
Using the “Plot Points” option and your line tool, graph the equation y 
-
Select ABC so the whole thing is highlighted (nothing else can be highlighted!)
-
Double click on the line y 
-
Under the “Transform” menu select “Reflect”
Answer questions a-c on your graph paper.
1
x3
3
1
x3
3
6. 90° Rotation about the origin:
- Delete everything on your screen except for your original triangle, ABC
- Select ABC so the whole thing is highlighted
- Double click on the origin.
- Under the “Transform” menu, select “Rotate”. Enter 90 into the textbox and click “Rotate”
- Answer questions a-d on your graph paper
7. 180° Rotation about the origin:
- Repeat the steps from problem 6, except rotate the figure 180° instead of 90°
- Answer questions a-d on your graph paper.
8. 270° Rotation about the origin:
- Repeat the steps from problem 6, except rotate the figure 270° instead of 90°
- Answer questions a-d on your graph paper
9. 86° Rotation about point (2, -1)
- Delete everything on your screen except for your original triangle, ABC
- Plot the point (2, -1)
- Select ABC so the whole thing is highlighted in pink
- Double click on the point (2, -1)
- Under the “Transform” menu, select “Rotate”. Enter 86 into the textbox and click “Rotate”
- Answer questions a-c on your graph paper.
10. Do your own rotation!!
- Pick your own point and your own degree measure and rotate ABC around that point!
- Answer questions a-c on your graph paper.