9.10 Rotations9.10 RotationsUnited Streaming Video

Dynamic Worksheets

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.

ExampleExampleRotate ABC with points A(1,-1) B(1,-4) C(5,-4) 90° about the origin.

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.

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.

Does a regular hexagon have rotational symmetry?

Yes, because 360 / 6 = 60. A hexagon has 60° rotational symmetry.

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

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