What is similar about these objects? What do we need to pay attention to when objects are rotated?
What is similar about these objects? What do we need to pay attention to when objects are rotated?
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Transcript of What is similar about these objects? What do we need to pay attention to when objects are rotated?
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)