**Geometry Unit 5, sec 7.3**

**Rotations - guided notes**

I) **Rotations** - sec. 7.3

A. **Definition**: A rotation is a transformation in which a figure is turned about a fixed point.

This point is called the center of rotation.

1. **Rotation 90 degrees** (counterclockwise): (x,y) maps to (** -y,x)**.

Example: (4 , 1) becomes (-1 , 4)

2. **Rotation 180 de**grees (counterclockwise): (x,y) maps to (* -x,-y*).

Example:(4 , 1) becomes (-4 , -1)

3. **Rotation 270 degrees** (counterclockwise) or -90 degrees (clockwise): (x,y) maps to (* y,-x*).

Example: (4 , 1) becomes (1 , -4)

B. **Rotational symmetry**: a figure has rotational symmetry if the figure can be mapped onto itself by a rotation of 180 degrees or less.

Example: A circle, Square, Rhombus, Equilateral Triangle, and more. **Any regular polygon with center angle 180 degrees or less.**

**An example of a figure without rotational symmetry: trapezoid**