Name:
Geometry L1 Transformations LAB Rotation (and Intro to Geogebra)
Date:
Period:
Pinwheels!
1. Go to http://www.geogebra.org/, click on “start creating” then “Geometry”. A blank
screen should pop up.
2. Click on the
to turn on the grid and axes.
3. Click on the
and the three dots to turn on the
“Algebra” panel on the left side of the screen.
4. Use the
axes.
to move the grid around and center your
5. Select the “polygon” command (looks like a triangle) and select
“polygon.” Create a triangle by clicking 3 points for each vertex and
then back on the first vertex to close the polygon. This should be
∆𝐴𝐵𝐶. The coordinates for A, B and C are located in the left
“Algebra” panel.
6. Rotate the triangle 60° about one of its vertices using the “rotate
around point” command. Click the triangle, the vertex to rotate
around, and then type in the angle of rotation. You should end
up with a new image and the pre-image. Rotate the image by
60° again to create a third triangle. Continue this process until
you complete the full circle. You have just made a pinwheel!
7. Explain how many points are on your pinwheel and why there
are that many.
8. Repeat this process to create pinwheels with 4, 5, and 8 points. Zoom out enough to get
all pinwheels to fit on one page. Save your worksheet as Last name, first initial,
Pinwheels (for example LaurenziAPinwheels). Print your worksheet (or email it to your
teacher).
9. Write a brief paragraph1 on your printout to describe how you created one of your
pinwheels. Be sure to explain how you got it to have the appropriate number of points.
1
A brief paragraph is between three and eight sentences.
Rotation about the origin
1. In a new worksheet (you will need to reestablish your axes, grid and algebra panel) use
the “polygon” command to create a new triangle (∆𝐴𝐵𝐶 ) in the first quadrant.
2. Add the point (0,0) using the
point command.
3. Rotate ∆𝐴𝐵𝐶 about the origin 90° using the “rotate around point” command. The image
should be ∆𝐴′𝐵′𝐶′. Record the coordinates of the pre-image and image in the table
below.
4. Rotate the pre-image about the origin 180° using the “rotate around point” command.
The image should be ∆𝐴′′𝐵′′𝐶′′. Record the coordinates in the table below.
5. Rotate the pre-image about the origin 270° using the “rotate around point” command.
The image should be ∆𝐴′′′𝐵′′′𝐶′′′. Record the coordinates in the table below.
Shape
∆𝐴𝐵𝐶
∆𝐴′𝐵′𝐶′
∆𝐴′′𝐵′′𝐶′′
∆𝐴′′′𝐵′′′𝐶′′′
Rotation
Pre-image
Coordinates
𝐴(
𝐴′(
𝐴′′(
𝐴′′′(
,
,
,
,
)
)
)
)
𝐵(
𝐵′(
𝐵′′(
𝐵′′′(
,
,
,
,
)
)
)
)
𝐶(
𝐶′(
𝐶′′(
𝐶′′′(
,
,
,
,
)
)
)
)
6. Use the data from your table to write a generic transformation rule for each rotation.
Rotation
Transformation
90°
(𝑥, 𝑦) → (
,
)
180°
(𝑥, 𝑦) → (
,
)
270°
(𝑥, 𝑦) → (
,
)
7. If point 𝑊(7, −2) was rotated 270° about the origin find the coordinates of 𝑊′.
8. Explain how you could use only 90° rotations to find the coordinates of a 270° rotation.