1. ROTATIONS (TURN OR SPIN)

2. All rotations will be counter-clockwise unless otherwise specified.
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.

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

4. 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.

5. 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.

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

7. Does a regular _____ have rotational symmetry?
Quadrilateral
360/4 = 90
Yes
Pentagon
360/5 = 72
Heptagon
360/7 = 5 1/7 No
Octagon
360/8 = 4.5
Nonagon
360/9 = 40
Decagon
360/10 = 36
Dodecagon
360/12 = 30

8. 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)