2.3 – Perform Rotations
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2.3 – Perform Rotations
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Rotation: Transformation that turns a figure about a fixed point
Center of Rotation:
The point that the rotation happens around
Angle of Rotation:
How many degrees clockwise or counterclockwise a shape is turned
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A rotation about a point P through an angle of x° maps every point Q in the plane to a point such that:
'Q
• If Q is not the center of rotation, then and 'QP Q P 'm QPQ x
x°
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A rotation about a point P through an angle of x° maps every point Q in the plane to a point such that:
'Q
• If Q is the center of rotation, then 'Q Q
Q 'Q
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Example #1: ROTATIONS ON A GRID Consider what you know about rotation, a motion that turns a shape about a point. Does it make any difference if a rotation is clockwise ( ) versus counterclockwise ( )? If so, when does it matter? Are there any circumstances when it does not matter? And are there any situations when the rotated image lies exactly on theoriginal shape?
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Investigate these questions as you rotate the shapes below about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above.
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- 180° doesn’t matter if you go clockwise or counterclockwise
- 90° counterclockwise is the same as 270 clockwise
- 360° rotates all the way around and matches the original shape
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Example #2: Rotate the triangle in the given degree about the origin.
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(2,2)'A
(5,5)'B
(5,2)
'C
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(2,2)'A
(5,5)
'B
(5,2)
'C
180
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(2,2)'A
(5,5)
'B
(5,2)
'C
270
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Example #3: State if the rotation about the origin is 90°, 180°, or 270° counter-clockwise.
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4. Find the value of each variable in the rotation.
x = 4
z = 3
y = z + 2y = 3 + 2y = 5
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4. Find the value of each variable in the rotation.
4s = 24s = 6
r = 2s – 3 r = 2(6) – 3
r = 9
r = 12 – 3