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Rotations Section 9.4

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Rotations A rotation is a transformation in which a figure is turned about a fixed point called the center of rotation. Rays drawn from the center of rotation to a point and its image form the angle of rotation.

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Coordinate Rules for Rotations about the Origin When a point (a, b) is rotated counterclockwise about the origin, the following are true: For a rotation of 90 o counterclockwise, (a, b)→(-b, a) For a rotation of 180 o counterclockwise, (a, b)→(-a, -b) For a rotation of 270 o counterclockwise, (a, b)→(b, -a) 90 o counterclockwise = 270 o clockwise 180 o counterclockwise = 180 o clockwise 270 o counterclockwise = 90 o clockwise If counterclockwise/clockwise is not stated, assume it is counterclockwise.

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Rotations Quadrilateral RSTU has vertices R(3, 1), S(5, 1), T(5, -3), and U(2, -1). What are the coordinates of the vertices after a rotation of 270 o counterclockwise about the origin.

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Rotations Trapezoid has vertices E(-3, 2), F(-3, 4), G(1, 4) and H(2, 2). Find the vertices of the image for a 180 o rotation about the origin.

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Rotations Trapezoid has vertices E(-3, 2), F(-3, 4), G(1, 4) and H(2, 2). Find the vertices of the image for a 90 o rotation clockwise about the origin.

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Assignment p.602: 3-11

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