Exploring Rotations:
Guided Notes
Light up
your learning!
Performing Rotations
while Graphing
1.
B
C
B’
A’
A
C’
Name: ______________________
Date: ____________
Preimage ABC is transformed into
image A’B’C’, after a 90° clockwise
rotation about the origin. Fill in the
table with the image points.
Preimage
Points
Image Points
A(−4, 2)
A’(____, ____)
B(−6, 7)
B’(____, ____)
C(−3, 6)
C’(____, ____)
What do you notice about the movement of the
triangle?
_______________________________________
_______________________________________
_______________________________________
What do you notice about the coordinates of
A’B’C’?
_______________________________________
_______________________________________
Each point in the preimage turns, or is rotated 90° clockwise, about the origin. A 90° angle is formed when the
preimage and image coordinates are connected through the origin. The preimage has turned into a new
position, creating an image. This specific turn is called a 90° clockwise rotation about the origin.
Coordinate Rule for the rotation in #1: __________________________________
Tip…flip-flop x and y, then change the sign on the new coordinate on the right (clockwise = right turn)
2.
Preimage ABC is transformed into image A’B’C’. The
image is rotated 90° clockwise about the origin. Draw
∆ ABC and then draw ∆ A’B’C’. Remember that the
preimage is undergoing a clockwise rotation.
Preimage
Points
Image Points
A(−3, −5)
A’(____, ____)
B(−5, −2)
B’(____, ____)
C(0, −1)
C’(____, ____)
Again, what do you notice about the coordinates of A’B’C’? This will help you remember the rule for this
rotation in coordinate notation.
Coordinate Rule for the rotation in #2: __________________________________
© Anna Taylor
http://www.teacherspayteachers.com/Store/Piece-Of-Pi
Tip…flip-flop, then change the sign on the new coordinate on the right (clockwise = right turn)
Exploring More Rotations:
Light up
your learning!
Performing Rotations
while Graphing
3.
B
C’
C
A’
B’
A
Preimage ABC is transformed into image
A’B’C’, after a 90° counterclockwise rotation
about the origin. Fill in the table with the
image points.
Preimage
Points
Image Points
A(3, 1)
A’(____, ____)
B(1, 6)
B’(____, ____)
C(5, 4 )
C’(____, ____)
What do you notice about the movement of the
triangle?
_______________________________________
_______________________________________
_______________________________________
What do you notice about the coordinates of
A’B’C’?
_______________________________________
_______________________________________
Each point in the preimage turns, or is rotated 90° counterclockwise, about the origin. A 90° angle is formed when
the preimage and image coordinates are connected through the origin. The preimage has turned into a new
position, creating an image. This specific turn is called a 90° counterclockwise rotation about the origin.
Coordinate Rule for the rotation in #3: __________________________________
Tip…flip-flop x and y, then change the sign on the new coordinate on the left (counterclockwise = left turn)
Preimage ABC is transformed into image A’B’C’. The
image is rotated 90° counterclockwise about the
origin. Draw ∆ ABC and then draw ∆ A’B’C’.
Remember that the preimage is undergoing a
counterclockwise rotation.
4.
Preimage
Points
Image Points
A(−3, −5)
A’(____, ____)
B(−5, −2)
B’(____, ____)
C(0, −1)
C’(____, ____)
Again, what do you notice about the coordinates of A’B’C’? This will help you remember the rule for this
rotation in coordinate notation.
Coordinate Rule for the rotation in #4: __________________________________
Tip…flip-flop x and y, then change the sign on the new coordinate on the left (counterclockwise = left turn)
© Anna Taylor
http://www.teacherspayteachers.com/Store/Piece-Of-Pi
Exploring More Rotations:
Light up
your learning!
Performing Rotations
while Graphing
5.
B
C
A
Preimage ABC is transformed into image
A’B’C’, after a 180° rotation about the
origin. Fill in the table with the image
points.
Preimage
Points
Image Points
A(3, 1)
A’(____, ____)
B(1, 6)
B’(____, ____)
C(5, 4 )
C’(____, ____)
What do you notice about the movement of the
triangle?
_______________________________________
_______________________________________
_______________________________________
A’
C’
B’
What do you notice about the coordinates of
A’B’C’?
_______________________________________
_______________________________________
Each point in the preimage turns, or is rotated 180° about the origin. A 180° angle is formed when the preimage and
image coordinates are connected through the origin. The preimage has turned into a new position, creating an
image. This specific turn is called a 180° rotation about the origin.
Coordinate Rule for the rotation in #5: __________________________________
Tip…just change the signs on x and y to get your new coordinates!
Question to consider: Why do you think it is unnecessary to state whether a 180° rotation is clockwise or
counterclockwise?
______________________________________________________________________________________
______________________________________________________________________________________
6.
Try another
180° rotation:
© Anna Taylor
http://www.teacherspayteachers.com/Store/Piece-Of-Pi
Preimage
Points
Image Points
A(5, −3)
A’(____, ____)
B(3, −1)
B’(____, ____)
C(0, −1)
C’(____, ____)
Extension: Exploring 270° Rotations
Believe it or not, you can rotate a figure
270° clockwise with the information you
already have!
How is this possible?
First, plot point A(2, 3). Then, complete a
90° clockwise rotation 3 times. Where is
your final image placed in the coordinate
plane?
After Clockwise 90° #1: A’__________
After Clockwise 90° #2: A’’_________
After Clockwise 90° #3: A’’’_________
What is 90•3? _____________
Now start over. If you rotated your
preimage A(2, 3) 90° counterclockwise,
what would be the coordinate of A’?
A’_____________
So…what have you discovered about 270° clockwise rotations?
________________________________________________________
Now, predict what will happen if you try to
complete a 270° counterclockwise rotation:
_________________________________________
_________________________________________
See if your prediction is accurate:
First, plot point B(3, 5). Then, complete a 90°
counterclockwise rotation 3 times. Where is your
final image placed in the coordinate plane?
B’__________ B’’_________ B’’’_________
If you started over again, and rotated your preimage B(3, 5) 90° clockwise, what would be the
coordinate of B’? B’____________
So…what have you discovered about 270° counterclockwise rotations?
________________________________________________________
© Anna Taylor
http://www.teacherspayteachers.com/Store/Piece-Of-Pi