Rotations - PowerPoint PPT Presentation

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Rotations. A rotation. turns all points of a figure around a point called the center of rotation the angle of rotation tells us the number of degrees through which points rotate around the center of rotation. Properties of rotations.

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Rotations

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Rotations

A rotation

• turns all points of a figure around a point called the center of rotation

• the angle of rotation tells us the number of degrees through which points rotate around the center of rotation

Properties of rotations

A rotation is a transformation about a point P such that

• every point and its image are the same distance from P and

• all angles with vertex P formed by a point and its image have the same measure

Notation

• The notation RP, m (A) = A’ says that the image of point A after a rotation of m degrees about point P is A’.

Rules for rotations in a coordinate plane

rotation of 90°:(x,y)  (-y,x)

rotation of 180°:(x,y)  (-x,-y)

rotation of 270°:(x,y)  (y,-x)

A positive angle of rotation turns the figure counterclockwise,

and a negative angle of rotation turns the figure in a clockwise direction.

Unless stated otherwise, rotations are counterclockwise.