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12-3 PPT Rotations.ppt - Wikispaces


									            Section 12-3 Transformations - Rotations
SPI 32D: determine whether the plane figure has been reflected given
a diagram and vice versa

  • Draw and identify rotation images of figures

                      Unit Overview
        Investigate Transformations
            Reflections (this lesson)
            Translations
            Rotations
            Composition of Transformations

• Type of transformation that turns a figure about a fixed

• Center of Rotation: fixed point

• An object and its rotation are the same shape and size,
but the figures may be turned in different directions.

                        Rotation of a polar star taken
                        during a 40-minute exposure
                                by a camera.
                Examples of Rotations

                   Riding a ferris wheel is an example of

Planetary movement is a
                  Describing a Rotation

Need to know:
• Center of rotation (a point)
• Angle of rotation (number of degrees)
• Whether rotation is clockwise or counterclockwise
              Geometric Definition of Rotation

A rotation of xº about a point R is a transformation for
which the following is true.
                 Drawing a Rotation Image

Copy ∆LOB, and draw its image
under a 60° rotation about C.

Step 1: Use a protractor to draw a 60° angle at vertex C
with one side CO.
                         … continued
 Step 2: Use a compass to construct CO’         CO.

Step 3: Locate L’ and B’ in a similar manner.
       Then draw L’ O’ B’ .
                     Identify a Rotation Image

                              Regular hexagon ABCDEF is
                              divided into six equilateral

a. Name the image of B for a 240° rotation about M.
   a. Because 360° ÷ 6 = 60°, each central angle of ABCDEF measures 60.
      A 240° counterclockwise rotation about center M moves point B across
      four triangles. The image of point B is point D.

b. Name the image of M for a 60° rotation about F.
   b.      AMF is equilateral, so AFM has measure 180 ÷ 3 = 60. A 60°
        rotation of AMF about point F would superimpose FM on FA, so the
        image of M under a 60° rotation about point F is point A.
                  Identify a Rotation Image
A regular 12-sided polygon can be formed by stacking
congruent square sheets of paper rotated about the same
center on top of each other. Find the angle of rotation about
M that maps W to B.

                  Consecutive vertices of the three squares form the
                  outline of a regular 12-sided polygon.

                  360 ÷ 12 = 30, so each vertex of the polygon is a 30°
                  rotation about point M.

                  You must rotate counterclockwise through 7 vertices
                  to map point W to point B, so the angle of rotation is
                  7 • 30°, or 210°.
               Compositions of Rotations

         Describe the image of quadrilateral XYZW for a
         composition of a 145° rotation and then a 215°
         rotation, both about point X.

The two rotations of 145° and 215° about the same point
is a total rotation of 145° + 215°, or 360°.

Because this forms a complete rotation about point X,
the image is the preimage XYZW.
Rotation Web

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