Geometry Rotations.

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Presentation transcript:

Geometry Rotations

Goals Identify rotations in the plane. Apply rotation formulas to figures on the coordinate plane. 12/7/2017

Rotation A transformation in which a figure is turned about a fixed point, called the center of rotation. Center of Rotation 12/7/2017

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

A Rotation is an Isometry Segment lengths are preserved. Angle measures are preserved. Parallel lines remain parallel. Orientation is unchanged. 12/7/2017

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

90 clockwise rotation Formula (x, y)  (y, x) A(-2, 4) A’(4, 2) 12/7/2017

Rotate (-3, -2) 90 clockwise Formula (x, y)  (y, x) A’(-2, 3) (-3, -2) 12/7/2017

90 counter-clockwise rotation Formula (x, y)  (y, x) A’(2, 4) A(4, -2) 12/7/2017

Rotate (-5, 3) 90 counter-clockwise Formula (x, y)  (y, x) (-5, 3) (-3, -5) 12/7/2017

180 rotation Formula (x, y)  (x, y) A’(4, 2) A(-4, -2) 12/7/2017

Rotate (3, -4) 180 Formula (x, y)  (x, y) (-3, 4) (3, -4) 12/7/2017

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

Rotation Example Rotate ABC 90 clockwise. Formula (x, y)  (y, x) 12/7/2017

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

Rotate ABC 90 clockwise. Check by rotating ABC 90. A’ B’ A(-3, 0) C’ C(1, -1) 12/7/2017

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