What is similar about these objects?
What do we need
to pay attention to
when objects are
rotated?
8-10 Transformations
What am I learning today?
Rotations
What will I do to show that I
learned it?
Determine coordinates and quadrant
resulting from a rotation.
Course 2
How do you determine the angle
of rotation?
A full turn is a 360° rotation.
A quarter turn is a 90°
rotation.
A half turn is a 180°
rotation.
360°
90°
270°
A three quarter turn is a
270° rotation.
What are they rotating around?
180°
8-10 Rotations
QUESTION
What do I need to know to
complete a rotation?
Course 2
8-10
Rotations
To rotate:
- the direction – CW or CCW
- the degrees – 90o, 180o, 270o
- the center or point of rotation –
origin or point inside the object
Course 2
8-10 Rotations
QUESTION
How do I rotate an object
in the coordinate plane?
Course 2
8-10 Rotations
To Rotate 180o around origin:
1. Keep your x- and y-values the
same.
.
2. Move to the opposite quadrant.
I to III
III to I
II to IV
IV to II
.
3. Put the appropriate signs
based on the quadrant.
Course 2
8-10
Rotations
Start: A (-4,3) in quadrant II
Rotate 180o clockwise
Finish: In quadrant IV, so x is
positive and y is
negative.
A’ (4,-3)
Course 2
8-10
Rotations
To Rotate 90o or 270o around origin:
1. x- and y-value switch places.
x becomes y and y becomes x.
.
2. Find the quadrant. Move one
for 90o or three for 270o. Pay
attention to the direction.
.
3. Put the appropriate signs
based on the quadrant.
Course 2
8-10
Rotations
Start: A (-4,3) in quadrant II
Rotate 270o clockwise
Finish: In quadrant III, so x is
negative and y is
negative.
A’ (-3,-4)
Course 2
8-10 Rotations
Rotations Around the Origin
Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0).
Rotate ∆ABC 90° counterclockwise about the origin.
C’
y
B’
B
3
A’
–3
Course 2
The pre-image coordinates of
triangle ABC are A(1,0), B(3, 3),
C(5,0).
A
Cx
The coordinates of the image of
triangle ABC are A’(0,1), B’(-3,3),
C’(0, 5).
Remember: A 90 degree rotation x and y
change places, then pay attention to the
characteristics of the quadrants.
8-10 Rotations
Rotations Around the Origin
Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0).
Rotate ∆ABC 180° counterclockwise about the origin.
The pre-image coordinates of
triangle ABC are A(1,0), B(3, 3),
C(5,0).
y
B
3
A
C’
A’
B’
Course 2
–3
Cx
The coordinates of the image of
triangle ABC are A’(-1, 0), B’(-3,-3),
C’(-5, 0).
Remember: A 180 degree rotation only
changes the signs, so pay attention to the
characteristics of the quadrants.
8-10 Rotations
Rotations Around the Origin
Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0).
Rotate ∆ABC 270° counterclockwise about the origin.
The pre-image coordinates of
triangle ABC are A(1,0), B(3, 3),
C(5,0).
y
B
3
Cx
A’
A
C’
B’
–3
Course 2
The coordinates of the image of
triangle ABC are A’(0,-1), B’(3,-3),
C’(0,-5).
Remember: A 270 degree rotation x and y
change places, then pay attention to the
characteristics of the quadrants.
K
rotation
I
M
Practice
Using these three points: P(6,3); C(-2,- 4); D(-1,0)
Rotate P 270o CCW
P’(3, -6)
Rotate C 90o CW
C’(-4,2)
Rotate D 180o CW
D’(1,0)
Rotate P 270o CW
P’(-3,6)
Rotate C 180o CCW
C’(2,4)
Rotate D 90o CW
D’(1,0)
Practice
Graph the pre-image, then rotate 90, 180, and 270 degrees
counterclockwise
P
Q
R
Now Try These
Graph Triangle MNL with vertices M(0,4), N(3,3), and
L(0,0). Rotate 90 degrees clockwise.
Graph Triangle ABC with vertices A(-3, -1), B(-3, -2), and
C(1, -2). Rotate 90 degrees clockwise.