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# Center of Rotation

You're probably already familiar with the term "rotation." After all, many things rotate, including the wheels on a car, the propeller of a plane, and the body of a spinning ballerina. But in the world of math, the term "rotation" has a more specific meaning. Let's find out more:

## The mathematical definition of rotation

When things rotate in the world of mathematics, they spin around a center. The distance between the center and any point on the spinning object remains the same. Every point on the shape also moves around the center in a perfect circle. The point never moves.

It helps to visualize this concept. Let's take a look at a diagram of a spinning object:

As we can see, the triangle is spinning around the center of rotation. Points A and B are spinning in such a way that their distance from the center of rotation remains the same throughout their motion. The center of rotation never moves.

The center of rotation plays a crucial role in understanding the geometry and mechanics of rotating objects. Apart from maintaining a constant distance between the center and any point on the object, several key properties and concepts are associated with the center of rotation:

• Invariant point: The center of rotation remains invariant, meaning it does not change its position during the rotation.
• Angle of rotation: The angle through which an object rotates around the center of rotation is called the angle of rotation. This angle can be measured in degrees or radians and can be either positive (counterclockwise) or negative (clockwise).
• Rotational symmetry: Some shapes exhibit rotational symmetry, which means they can be rotated around their center of rotation by a certain angle and still look the same. For example, a square has rotational symmetry of order 4, as it can be rotated by 90, 180, or 270 degrees and maintain its appearance.
• Coordinate transformations: In a coordinate plane, the center of rotation can be represented by a pair of coordinates (h, k). When rotating a point (x, y) around this center by a specific angle, we can apply coordinate transformation equations to find the new coordinates of the rotated point.

## Topics related to the Center of Rotation

Angle of Rotation

Rotational Symmetry

Rotations

## Flashcards covering the Center of Rotation

Common Core: High School - Geometry Flashcards

## Practice tests covering the Center of Rotation

Common Core: High School - Geometry Diagnostic Tests