Rotations.

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Presentation transcript:

Rotations

Where have you experienced a rotation? What is a rotation? Where have you experienced a rotation?

A rotation A transformation that TURNS all points of a figure around a fixed point called the Center of rotation

Angle of Rotation The angle of rotation tells us the number of degrees through which points rotate around the center of rotation A positive angle of rotation turns the figure counterclockwise, and a negative angle of rotation turns the figure in a clockwise direction.

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 (lie on a circle)and all angles with vertex P formed by a point and its image have the same measure http://www.mathsisfun.com/geometry/rotation.html

Notation RP, θ (ABC) =  A’B’C’ The notation RP, θ (A) = A’ says that the image of point A after a rotation of θ degrees about point P is A’. θ is the Greek symbol THETA and is used to for angle measures. If the point is not specified, it is the origin. Note that reflections are written with a capital R. RP, θ (ABC) =  A’B’C’

Rules for rotations in a coordinate plane around the origin Rotation of 90°: R90°(x,y)  (-y,x) OYX Rotation of 180°: R180° (x,y)  (-x,-y) OXOY Rotation of 270°: R270° (x,y)  (y,-x) YOX

http://www.regentsprep.org/Regents/math/geometry/GT4/PracRot.htm Try it yourself! http://www.shodor.org/interactivate/activities/Transmographer/