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ROTATION
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12/7/2015 Goals Identify rotations in the plane. Apply rotation to figures on the coordinate plane.
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12/7/2015 Rotation A transformation in which a figure is turned about a fixed point, called the center of rotation. Center of Rotation
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The center of rotation could be a point outside the shape or on the shape A ROTATION MEANS TO TURN A FIGURE center of rotation
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ROTATION A ROTATION MEANS TO TURN A FIGURE The triangle was rotated around the point. center of rotation
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ROTATION If a shape spins 360 , how far does it spin? 360
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ROTATION If a shape spins 180 , how far does it spin? 180 Rotating a shape 180 turns a shape upside down.
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ROTATION If a shape spins 90 , how far does it spin? 90
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ROTATION Describe how the triangle A was transformed to make triangle B AB Describe the translation. Triangle A was rotated right 90
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ROTATION Describe how the arrow A was transformed to make arrow B Describe the translation. Arrow A was rotated right 180 A B
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12/7/2015 Rotation Rays drawn from the center of rotation to a point and its image form an angle called the angle of rotation. Center of Rotation 90 G G’
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12/7/2015 A Rotation is an Isometry (Rigid Transformation) Segment lengths are preserved. Angle measures are preserved. Parallel lines remain parallel. Orientation is unchanged.
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12/7/2015 Rotations on the Coordinate Plane Be able to do: 90 rotations 180 rotations clockwise & counter- clockwise Unless told otherwise, the center of rotation is the origin (0, 0).
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12/7/2015 90 clockwise rotation Formula (x, y) (y, x) A(-2, 4) A’(4, 2) Or… Use the relation between the slopes of two perpendicular lines
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12/7/2015 Rotate (-3, -2) 90 clockwise Formula (x, y) (y, x) (-3, -2) A’(-2, 3) Or… Use the relation between the slopes of two perpendicular lines
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12/7/2015 90 counter-clockwise rotation Formula (x, y) ( y, x) A(4, -2) A’(2, 4)
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12/7/2015 Rotate (-5, 3) 90 counter-clockwise Formula (x, y) ( y, x) (-3, -5) (-5, 3)
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12/7/2015 180 rotation Formula (x, y) ( x, y) A(-4, -2) A’(4, 2)
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12/7/2015 Rotate (3, -4) 180 Formula (x, y) ( x, y) (3, -4) (-3, 4)
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12/7/2015 Rotation Example Draw a coordinate grid and graph: A(-3, 0) B(-2, 4) C(1, -1) Draw ABC A(-3, 0) B(-2, 4) C(1, -1)
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12/7/2015 Rotation Example Rotate ABC 90 clockwise. Formula (x, y) (y, x) A(-3, 0) B(-2, 4) C(1, -1)
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12/7/2015 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(-3, 0) B(-2, 4) C(1, -1) A’ B’ C’
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12/7/2015 Rotate ABC 90 clockwise. Check by rotating ABC 90 . A(-3, 0) B(-2, 4) C(1, -1) A’ B’ C’
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12/7/2015 Rotation Formulas 90 CW(x, y) (y, x) 90 CCW(x, y) ( y, x) 180 (x, y) ( x, y) These rules only work when the center of rotation is the origin. Use the opposite reciprocal relation between the slopes of perpendicular lines to do rotations about other points.
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12/7/2015 Rotating segments A B C D E F G H O
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12/7/2015 Rotating AC 90 CW about the origin maps it to _______. A B C D E F G H CE O
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12/7/2015 Rotating HG 90 CCW about the origin maps it to _______. A B C D E F G H FE O
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12/7/2015 Rotating AH 180 about the origin maps it to _______. A B C D E F G H ED O
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12/7/2015 Rotating GF 90 CCW about point G maps it to _______. A B C D E F G H GH O
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12/7/2015 Rotating ACEG 180 about the origin maps it to _______. A B C D E F G H EGAC AE C G O
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12/7/2015 Rotating FED 270 CCW about point D maps it to _______. A B C D E F G H BOD O
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12/7/2015 Summary A rotation is a transformation where the preimage is rotated about the center of rotation. Rotations are Rigid Transformations
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12/7/2015
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Homework
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