Name: ____________________________________ Date: _______________ Period: ___________
Rotations
Part 1:
1. In the grid below, 𝐴𝐵𝐶 has been rotated 30⁰ counterclockwise with the center of rotation at the origin. This process was
repeated several times to create the images shown.
10
8
6
B
4
A
20
15
10
C
2
5
5
2
4
6
8
10
2. Label the corresponding parts of the images of ABC.
3. Describe the properties of a rotation based on what you see.
10
15
20
Part 2:
Directions: Describe the rotation that has taken place.
4.
10
8
B
A'
6
4
B'
C'
2
A
20
15
C
10
5
5
10
15
20
2
4
6
8
10
5.
10
8
S
T
6
4
R
U
2
20
15
10
5
5
2
U'
R'
4
6
T'
S'
8
10
10
15
20
6. Rotate ABCD 90⁰ clockwise with the center of rotation at the origin.
8
6
A
B
4
2
D
10
C
5
5
10
5
10
2
4
6
8
7. Rotate ABC 180⁰ counterclockwise with the center of rotation at (1, 1).
8
B
6
4
2
A
10
5
2
4
6
8
C
̅̅̅̅ 90⁰ counterclockwise with the center of rotation at the origin.
8. Rotate 𝑃𝑄
10
8
P
6
4
2
20
15
10
Q
5
5
10
15
20
5
10
15
20
2
4
6
8
10
9. Rotate ABC 180⁰ clockwise with the center of rotation at A.
10
8
6
4
B
2
A
20
15
10
C
5
2
4
6
8
10
10. Below are some pairs of congruent line segments. We know they are congruent because,
for each pair, we were able to find a center of rotation and rotate the segment on the
right so it fit exactly on the segment to the left. We tried several possible points for
this first segment pair and we think we’ve found a center of rotation.
a. Check to see if our point is correct.
Place a piece of patty paper over the 2 segments.
■ Trace the segment on the right and our point onto the patty paper.
■ Use your pencil to anchor the patty paper at the point and rotate the patty paper to see
if the traced segment lands on top of the segment on the left.
■
b. Find centers of rotation for the segment pairs below. Use the method outlined above to
check your centers.
You may have tried several points, and many did not work. Describe how you found a
center of rotation that worked.
c. Point A is 1 center of rotation. (Check with your patty paper.) A rotation of 90 degrees
will do it. There is another point that also serves as a center of rotation. Where is that
point, and how did you find it?
d. Find 2 different centers of rotation for the segments below. How did you find each
center?
e. Find 2 different centers of rotation for the segments below. How did you find each
center?