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Rotations

A rotation is a transformation in a plane that turns every point of a preimage through a specified angle and direction about a fixed point. The fixed point is called the center of rotation . The amount of rotation is called the angle of rotation and it is measured in degrees. Use a protractor to measure the specified angle counterclockwise.

Some simple rotations can be performed easily in the coordinate plane using the rules below.

Rotation by $90°$ about the origin:

A rotation by $90°$ about the origin is shown.

The rule for a rotation by $90°$ about the origin is $(x,y)\to (-y,x)$ .

Rotation by $180°$ about the origin:

A rotation by $180°$ about the origin is shown.

The rule for a rotation by $180°$ about the origin is $(x,y)\to (-x,-y)$ .

Rotation by $270°$ about the origin:

A rotation by $270°$ about the origin is shown.

The rule for a rotation by $270°$ about the origin is $(x,y)\to (y,-x)$ .