Course 2
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.
A full turn is a 360° rotation.
90°
180°
360°
How do you determine the How do you determine the angle of rotation?angle of rotation?
What are they rotating around?
270°
A quarter turn is a 90° rotation.
A half turn is a 180° rotation.
A three quarter turn is a 270° rotation.
To rotate:
Course 2
8-10 Rotations
- 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
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)
Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0). Rotate ∆ABC 90° counterclockwise about the origin.
Rotations Around the Origin
Course 2
8-10 Rotations
x
y
A
B
C
3
–3
The pre-image coordinates of triangle ABC are A(1,0), B(3, 3), C(5,0).
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.
C’
B’
A’
Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0). Rotate ∆ABC 180° counterclockwise about the origin.
Rotations Around the Origin
Course 2
8-10 Rotations
x
y
A
B
C
3
–3
C’
B’
A’
The pre-image coordinates of triangle ABC are A(1,0), B(3, 3), C(5,0).
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.
Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0). Rotate ∆ABC 270° counterclockwise about the origin.
Rotations Around the Origin
Course 2
8-10 Rotations
x
y
A
B
C
3
–3
The pre-image coordinates of triangle ABC are A(1,0), B(3, 3), C(5,0).
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.C’
B’
A’
PracticeUsing these three points: P(6,3); C(-2,- 4); D(-1,0)
Rotate P 270o CCW
Rotate C 90o CW
Rotate D 180o CW
Rotate P 270o CW
Rotate C 180o CCW
Rotate D 90o CW
P’(3, -6)
C’(-4,2)
D’(1,0)
P’(-3,6)
C’(2,4)
D’(1,0)
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