9.10 Rotations

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9.10 Rotations
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A rotation is a transformation that turns a
figure about a fixed point called the center of
rotation.
The measure of the rotation is the angle of
rotation.
All rotations will be counter-clockwise unless
otherwise specified.
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Example
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Rotational Symmetry
A figure has rotational symmetry if you can
rotate it 180, or less, so that its image
matches the original figure.
The angle (or its measure) through which the
figure rotates is the angle of rotation.
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To find the Angle of Rotation
If a figure has rotational symmetry, find the
angle of rotation by dividing 360 by how many
times the figure matches itself.
A regular triangle will have 120 rotational
symmetry because 360 / 3 120.
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Does a regular hexagon have rotational symmetry?
Yes, because 360 / 6 60. A hexagon has 60
rotational symmetry.
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Does a regular _____ have rotational symmetry?
Quadrilateral 360/4 90 Yes
Pentagon 360/5 72 Yes
Heptagon 360/7 5 1/7 No
Octagon 360/8 4.5 No
Nonagon 360/9 40 Yes
Decagon 360/10 36 Yes
Dodecagon 360/12 30 Yes
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Things to Remember about rotations
90 (x, y) -gt (-y, x)
180 (x, y) -gt (-x, -y)
270 (x, y) -gt (y, -x)
For Example B(2, 3) 90 B (-3, 2) 180
B (-2, -3) 270 B(3, -2) 360 B(2, 3)
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