Rotations of points, shapes

In math, a rotation lives up to its name!

To rotate an object you need a center of rotation and how much you want to rotate it. By convention, positive rotations go counter clockwise, and negative rotations go clockwise.

Interactive demonstration

of How to Perform a Rotation in Math

The demonstration below that shows you how to easily perform the common Rotations (ie rotation by 90 , 180 , or rotation by 270) . There is a neat 'trick' to doing these kinds of transformations. The basics steps are to graph the original point (the pre-image), then physically 'rotate' your graph paper, the new location of your point represents the coordinates of the image. It's much easier to understand these steps if you watch the visual demonstration below.

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Rotation notation is usually denoted R(center , degrees)

  • "Center" is the 'center of rotation.' This is the point around which you are performing your mathematical rotation.
  • "Degrees" stands for how many degrees you should rotate. A positive number usually by convention means counter clockwise.

Very often rotations are performed using coordinate notation as they all are on this page. The coordinates allow us to easily describe the image and its preimage.

Examples of the most common rotations

Rotation by 90° about the origin: R(origin, 90°)

A rotation by 90° about the origin can be seen in the picture below in which A is rotated to its image A'. The general rule for a rotation by 90° about the origin is (A,B) (-B, A)

picture of rotation by 90 degrees about origin

Rotation by 180° about the origin: R(origin, 180°)

A rotation by 180° about the origin can be seen in the picture below in which A is rotated to its image A'. The general rule for a rotation by 180° about the origin is (A,B) (-A, -B)

picture of rotation by 180 degrees about origin

Rotation by 270° about the origin: R(origin, 270°)

A rotation by 270° about the origin can be seen in the picture below in which A is rotated to its image A'. The general rule for a rotation by 270° about the origin is (A,B) (B, -A)

picture of rotation by 270 degrees about origin

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Use the interactive demonstration below to see how to rotate a point about the origin.

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