Geometry
Notes: Rotations
Rotate:________________________________________________________
Clockwise (CW):
Counterclockwise (CCW):
There are _________ degrees in a circle. When we rotate clockwise or
counterclockwise, the two rotations should always add up to _________ degrees.
Examples
What rotation will take P to P’?
1.
2.
P
C
3.
P
75 
C
P’
C
P’
40 
P
P’
CW _______
CCW ______
4.
CW _______
CCW ______
Which figure is a rotation of the original?
a)
5.
CW ______
CCW _____
b)
c)
Which figure is a rotation of the original?
a)
b)
c)
Rules of Rotation
1.
Y
T
180  CW or 180  CCW
(x, y)  (x, y)
90  CCW or 270  CW
(x, y)  (y, x)
T ________
T’ ________
R ________
R’ ________
Y ________
Y’ ________
Rotate TRY 90  CCW from the origin. Call it T’R’Y’.
R
Y
T
3.
(x, y)  (y, x)
Rotate TRY 90  CW from the origin. Call it T’R’Y’.
R
2.
90  CW or 270  CCW
T ________
T’ ________
R ________
R’ ________
Y ________
Y’ ________
Rotate TRY 180  CW from the origin. Call it T’R’Y’.
R
Y
T
T ________
T’ ________
R ________
R’ ________
Y ________
Y’ ________
4.
a.
Rotate 270  CW from the origin.
Call it H’A’T’.
H _______
H’ _______
A _______
A’ _______
T _______
T’ _______
H
A
b.
H” _______
c.
T
Reflect over the line x  1 .
Call it H”A”T”.
A” _______
T” _______
Translate 3 right and 4 down.
Call it BUG.
B _______
U _______
Translation
Is congruency
preserved?
Is orientation
preserved?
G _______
Reflection
Rotation
Geometry
Rotations Worksheet
Name: _______________________
Rules of Rotation
1.
90  CW or 270  CCW
(x, y)  (y, x)
180  CW or 180  CCW
(x, y)  (x, y)
90  CCW or 270  CW
(x, y)  (y, x)
Rotate LEG 90  CW from the origin. Call it L’E’G’.
L
L ________
L’ ________
E ________
E’ ________
G ________
G’ ________
E
G
2.
Rotate TOE 270  CW from the origin. Call it T’O’E’.
T
O
E
T ________
T’ ________
O ________
O’ ________
E ________
E’ ________
3.
Rotate 180  CCW from the origin. Call it L’I’P’.
L
P
4.
a.
L’ ________
I ________
I’ ________
P ________
P’ ________
I
Rotate 270  CW from the origin.
Call it F’U’N’.
F _______
b.
F
F’ _______
U _______
U’ _______
N _______
N’ _______
U
N
Reflect over the line x  1 .
Call it F”U”N”.
F” _______
c.
U” _______
N” _______
Translate 2 right and 5 up.
Call it TYM.
T _______
5.
L ________
Y _______
M _______
What rotation will take P to P’?
P
a.
b.
C
c.
P
35 
C
P’
CW _______
CCW ______
CW _______
CCW ______
P’
P’
C
20 
P
CW ______
CCW _____
6.
Which figure is a rotation of the original?
a)
7.
b)
c)
Which figure is a rotation of the original?
a)
b)
c)
Give the new coordinate after each rotation.
8.
90  CW
M(2, 0)
A(-3, 4)
T(5, 2)
H(-1, 6)
10.
9.
M’________
A’________
T’________
H’________
270  CW
G(3, 5)
E(-6, 3)
O(1, 2)
M(-42, 5)
T(3, 2)
R(7, -1)
I(4, 0)
G(2, 8)
11.
G’________
E’________
O’________
M’________
180  CW
T’________
R’________
I’________
G’________
360  CW
A(-56, 0)
L(24, 3)
G(6, -7)
A’________
L’________
G’________