9.10 Rotations 9.10 Rotations United Streaming Video Dynamic Worksheets.

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Presentation transcript:

9.10 Rotations 9.10 Rotations United 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.

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

Rotational Symmetry 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.

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.

Does a regular hexagon have rotational symmetry? Yes, because 360 / 6 = 60. A hexagon has 60° rotational symmetry.

Does a regular _____ have rotational symmetry? Quadrilateral360/4 = 90Yes Pentagon360/5 = 72Yes Heptagon360/7 = 5 1/7No Octagon360/8 = 4.5No Nonagon360/9 = 40Yes Decagon360/10 = 36Yes Dodecagon360/12 = 30Yes

Things to Remember about 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