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Geometry Rotations
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Goals Identify rotations in the plane.
Apply rotation formulas to figures on the coordinate plane. 12/7/2017
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Rotation A transformation in which a figure is turned about a fixed point, called the center of rotation. Center of Rotation 12/7/2017
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Rotation Rays drawn from the center of rotation to a point and its image form an angle called the angle of rotation. G 90 Center of Rotation G’ 12/7/2017
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A Rotation is an Isometry
Segment lengths are preserved. Angle measures are preserved. Parallel lines remain parallel. Orientation is unchanged. 12/7/2017
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Rotations on the Coordinate Plane
Know the formulas for: 90 rotations 180 rotations clockwise & counter-clockwise Unless told otherwise, the center of rotation is the origin (0, 0). 12/7/2017
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90 clockwise rotation Formula (x, y) (y, x) A(-2, 4) A’(4, 2)
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Rotate (-3, -2) 90 clockwise
Formula (x, y) (y, x) A’(-2, 3) (-3, -2) 12/7/2017
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90 counter-clockwise rotation
Formula (x, y) (y, x) A’(2, 4) A(4, -2) 12/7/2017
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Rotate (-5, 3) 90 counter-clockwise
Formula (x, y) (y, x) (-5, 3) (-3, -5) 12/7/2017
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180 rotation Formula (x, y) (x, y) A’(4, 2) A(-4, -2) 12/7/2017
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Rotate (3, -4) 180 Formula (x, y) (x, y) (-3, 4) (3, -4)
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Rotation Example Draw a coordinate grid and graph: A(-3, 0) B(-2, 4)
Draw ABC A(-3, 0) C(1, -1) 12/7/2017
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Rotation Example Rotate ABC 90 clockwise. Formula (x, y) (y, x)
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Rotate ABC 90 clockwise.
(x, y) (y, x) A(-3, 0) A’(0, 3) B(-2, 4) B’(4, 2) C(1, -1) C’(-1, -1) A’ B’ A(-3, 0) C’ C(1, -1) 12/7/2017
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Rotate ABC 90 clockwise.
Check by rotating ABC 90. A’ B’ A(-3, 0) C’ C(1, -1) 12/7/2017
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Rotation Formulas 90 CW (x, y) (y, x) 90 CCW (x, y) (y, x)
180 (x, y) (x, y) Rotating through an angle other than 90 or 180 requires much more complicated math. 12/7/2017
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