Name: _______________________________________
Imagine That!!
DIRECTIONS: Use Geometer’s Sketchpad to answer the following questions about transformations.
Write your answers on a separate piece of paper. You may work with the people around you but each of
your will turn in your own work. Your work will be collected at the end of the class period.
1. Start by opening a new window in Geometer’s Sketchpad.
Under the “Graph” menu at the top, select “Show Grid”.
2. Construct a trapezoid:
- To plot a new point, select “Plot Points” under the “Graph” menu tab.
o Plot the points A(1, 1), B(1, 3), C(7, 3), and D(5, 1)
o After all the points are plotted, click the “done” button.
- Highlight each of the four points you just constructed by clicking on each point, starting with
the point (1, 1) and moving clockwise.
- Under the “Construct” menu tab, select “Segments”.
- You should have a trapezoid that looks like this:
4
2
5
10
-2
For Problems 3 – 8, answer the following questions:
a) Sketch and describe the transformation that was performed. How did your original image
change?
b) Record the coordinates for the new image A’B’C’D’. How do the coordinates of the new
image compare to the original coordinates?
c) Write a general rule to show how the coordinates change.
3. Reflection over the x-axis:
- Select your trapezoid so the whole thing is highlighted in pink.
- Double click on the x-axis
- Under the “Transform” menu tab, select “Reflect”.
Name: _______________________________________
4. Reflection over the y-axis:
- Delete your previous reflection (do not delete your original image).
- Select your original trapezoid so the whole thing is highlighted in pink.
- Double click on the y-axis
- Under the “Transform” menu tab, select “Reflect”.
5. 90° counterclockwise rotation:
- Delete your previous reflection (do not delete your original image).
- Select your original trapezoid to the whole thing is highlighted in pink.
- Double click on the origin.
- Under the “Transform” menu tab, select “Rotate”. Enter “90” into the textbox and click
“Rotate”.
6. 180° rotation:
- Don’t delete your previous rotation before rotating the original trapezoid 180°.
- Repeat the steps from problem 5, except rotate the figure 180° instead of 90°.
7. 270° counterclockwise rotation:
- Don’t delete your previous rotations before rotating the original trapezoid 270°.
- Repeat the steps from problem 5, except rotate the figure 270° instead of 90°.
8. Translation:
- Delete all of your rotations, leaving only your original trapezoid
- Select your original trapezoid so the whole thing is highlighted in pink.
- Under “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.
Name: _______________________________________
For Problems 9 and 10, open a new sketch under the “File” menu tab. Select “Show Grid” under the
“Graph” menu tab. Plot the points E(0, 0), F(2, 4), G(5, 1), and H(3, 0). Connect the points EFGH with
line segments to create your new quadrilateral:
4
2
5
-2
9. Dilation:
- Select your quadrilateral so the entire thing is highlighted in pink. (Make sure the
quadrilateral is the ONLY thing that is highlighted.)
- Under the “Transform” menu tab, select “Dilation”. For your fixed ratio, enter 3 over 1.
Click the “Dilate” button.
a) Sketch and describe the transformation that was performed. How did your original image
change?
b) Record the coordinates for the new image E’F’G’H’. How do they compare to the original
coordinates?
c) Click on the points E and F so that they are highlighted. Under the “Measure” menu tab select
“Distance”. What is the distance between those two points?
d) Now find the distance between the points E and F’. How does that distance compare to the
distance between E and F?
e) Find the slope of the line EF. Find the slope of the line EF’. How do the two slopes compare?
10. Dilation Part II:
1
a) Describe what you think would happen if you entered a fixed ratio of 2 instead of 3 over 1?
b) Test your prediction. Were you right? Why or why not?
Name: _______________________________________
11. The coordinates of quadrilateral ABCD are listed below in a matrix.
A
B
C D
3 −2 −3 5
[
]
5 4
1 1
a) Use matrix multiplication to transform ABCD. (Multiply using your calculator.)
A
B
C D
1 0 3 −2 −3 5
[
][
]
0 −1 5 4
1 1
b) Plot the quadrilateral ABCD in Geometer’s Sketchpad
c) Plot the image A’B’C’D’ in Geometer’s sketchpad. What kind of transformation was
performed?