Rotation in math is a concept originating in geometry that describes the circular movement of an object around a center or an axis. It is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point. The distance from the center to any point on the shape stays the same, and every point makes a circle around the center. The result of a rotation is a new figure, called the image, which is congruent to the original figure.
Some key points about rotation in math include:
- Angle: A rotation can be clockwise (negative) or counterclockwise (positive) and is measured in degrees.
- Center of Rotation: The figure can rotate around any given point, known as the center of rotation.
- Image: The result of a rotation is a new figure, called the image, which is congruent to the original figure.
Rotations can be performed on any shape, and the rotation can be any number of degrees, although it will usually be a common angle such as 90 or 180 degrees. Rotations can be described mathematically using matrices, and all rotations about a fixed point form a group under composition called the rotation group).
