9.10 rotations 9.10 rotations united streaming video dynamic worksheets
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9.10 Rotations9.10 RotationsUnited Streaming Video
Dynamic Worksheets
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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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ExampleExampleRotate ABC with points A(1,-1) B(1,-4) C(5,-4) 90° about the origin.
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Rotational SymmetryRotational SymmetryA 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 To find the Angle of RotationRotationIf 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?
QuadrilateralQuadrilateral 360/4 = 90 YesYes
PentagonPentagon 360/5 = 72 YesYes
HeptagonHeptagon 360/7 = 5 1/7
NoNo
OctagonOctagon 360/8 = 4.5 NoNo
NonagonNonagon 360/9 = 40 YesYes
DecagonDecagon 360/10 = 36 YesYes
DodecagonDodecagon 360/12 = 30 YesYes
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Things to Remember about Things to Remember about rotations…rotations…90° (x, y) -> (-y, x)
180° (x, y) -> (-x, -y)
270° (x, y) -> (y, -x) For Example: B(2, 3)90° B’ (-3, 2)180° B” (-2, -3)270° B”’(3, -2)360° B””(2, 3)Hot Potatoes