Exploration on Rotations
Part I. The figure below has been rotated 90 clockwise. Compare the pre-image ABCDE
and the image A’B’C’D’E’. Explain relationships:
bout the origin
kwise about the origin
1) How do the sizes compare?
2) How do the orientations (direction
they are “faced”) compare?
3) Complete the table below.
Coordinates of Pre Image
Points
Coordinates of Image
Points
4) Explain how you could draw
A
A’
the image from knowing
B
B’
C
C’
D
D’
E
E’
the pre-image points.
5) Rule is (𝑥, 𝑦) →
(_________, _________)
10
8
B'
D
6
C
C'
A'
4
E
B
D'
2
E'
10
5
5
A
2
4
6
10
wise about the origin
Part II. The figure below has been rotated 90 counterclockwise. Compare the pre-image
ABCDE and the image A’B’C’D’E’. Explain relationships:
8) Complete the table below.
Coordinates of Pre Image
Points
Coordinates of Image
Points
9) Explain how you could draw
A
A’
the image from knowing
B
B’
C
C’
D
D’
E
E’
the pre-image points.
10)
Rule is (𝑥, 𝑦) → (_________, _________)
8
D
6
C
4
E
B
2
10
5
5
A
E'
2
D'
4
A'
6
C'
B'
8
10
out the origin
Part III. The figure below has been rotated 180 degrees. Compare the pre-image
ABCDE and the image A’B’C’D’E’. Explain relationships:
13) Complete the table below.
Coordinates of Pre Image
Points
14) Explain how you could
draw the image from
knowing the pre-image
points.
15) Rule is
Coordinates of Image
Points
A
A’
B
B’
C
C’
D
D’
E
E’
(𝑥, 𝑦) → (_________, _________)
8
D
6
C
4
E
B
2
A'
10
5
5
A
10
2
E'
B'
4
C'
6
D'
8
Check your “rules” with your teacher to make sure that you found the correct patterns
BEFORE you try this on your own.
Now, try it yourself.
For each rotation below, identify the pre-image points then record their images after the
described rotation.
Rotate Counterclockwise 90 degrees
10
-10 -8 -6 -4 -2
Rotate 180 degrees
10
8
8
6
6
4
4
2
2
A
2
4
6
8 10
-10 -8 -6 -4 -2
A
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
Rotate Clockwise 90 degrees
10
8
6
4
2
-10 -8 -6 -4 -2
A
-2
-4
-6
-8
-10
2
4
6
8 10
2
4
6
8 10