Rotation

Rotation in mathematics refers to the movement of a figure around a fixed point. The fixed point is called the center of rotation. When a figure is rotated, its size and shape remain the same, but its position changes.

Key Concepts

1. Center of Rotation: The fixed point around which the figure is rotated.
2. Angle of Rotation: The amount of rotation, measured in degrees, from the original position to the final position of the figure.
3. Direction of Rotation: Clockwise or counterclockwise rotation, determined by the direction in which the figure moves around the center of rotation.

Types of Rotations

There are two main types of rotations:

1. Clockwise Rotation: The figure moves in the direction of a clock's hands.
2. Counterclockwise Rotation: The figure moves in the opposite direction to a clock's hands.

Rotation Notation

Rotations can be described using notation. For example, a 90-degree counterclockwise rotation of a figure F around point P can be denoted as "R_P,90°(F)".

Properties of Rotations

Some important properties of rotations include:

1. Rotating a figure multiple times around the same center results in cumulative rotations.
2. Rotating a figure 180 degrees results in its reflection over the center of rotation.

Study Guide

When studying rotations, it is important to practice the following:

1. Identifying the center of rotation in a given figure.
2. Determining the angle and direction of rotation required to move a figure to a specific position.
3. Understanding the effects of multiple rotations on a figure.
4. Using rotation notation to describe and perform rotations.