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Rotation

Rotation

One-page printable reference

See It in Action

Two examples of the idea done right—and one common look-alike that is not right.

EXAMPLE

EXAMPLE

NON-EXAMPLE

Definition

A rotation is a transformation that turns a figure around a fixed point, called the center of rotation, through a specified angle and direction.

Key Points:

  • It is a type of rigid motion, meaning the figure’s size and shape stay the same.

  • The center of rotation does not move.

  • Each point in the figure moves along a circular arc around the center.

  • The angle of rotation tells how far the figure is turned (e.g., 90°, 180°, 270°).

  • A positive angle means counterclockwise rotation.

  • A negative angle means clockwise rotation.

Example:

Rotating a rectangle 180° about the origin turns the entire shape around the origin, producing an image that is congruent but in a new orientation.


A rectangle and its image in the coordinate plane after a 180 degree rotation. The original figure is in the first quadrant, and the image is in the third quadrant.

Video


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