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Last Updated Sep 27, 2025

Rotations Simplified Revision Notes

Revision notes with simplified explanations to understand Rotations quickly and effectively.

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Rotations

What is Rotation?

Rotation involves turning a shape around a specific point, called the centre of rotation, by a certain angle, in either a clockwise or anti-clockwise direction.

Key Characteristics of Rotation:

  • The image (rotated shape) is the same size as the original but may be in a different orientation.
  • The distance from the centre of rotation to any point on the shape remains the same before and after the rotation.
  • Angle of rotation: This is typically 90°,180°,or 270°90°, 180°, or\ 270°.
  • Direction of rotation: This can be clockwise or anti-clockwise.
image

Describing Rotations

When describing a rotation, you must provide the following information:

  1. Centre of Rotation: This is the fixed point around which the shape is rotated. It is often given as a coordinate, such as (0,00, 0) or (2,12, 1).
  2. Direction of Rotation: This is the degree of rotation, which is usually 90°,180°90°, 180°, or 270°270°.
  3. Angle of Rotation: This is the degree of rotation, which is usually 90°,180°90°, 180°, or 270°270°.
infoNote

Worked Example 1: Rotating Around the Origin (0,00, 0)

Rotate the blue object to obtain the purple object with the following details:

  • Centre of Rotation: (0,00, 0) - the origin
  • Direction of Rotation: Clockwise
  • Angle of Rotation: 90°90° Steps:
  1. Locate the centre of rotation at (0,00, 0) on the grid.
  2. Rotate each point of the blue object 90°90° clockwise around the origin.
  3. Plot the new points and draw the purple object. Notice: If you wanted to describe the same rotation differently, you could say it was a 270°270° anti-clockwise rotation since both produce the same result.
infoNote

Worked Example 2: Rotating Around a Point (2,12, 1)

Rotate the blue object to obtain the purple object with the following details:

  • Centre of Rotation: (2,12, 1)
  • Direction of Rotation: Clockwise
  • Angle of Rotation: 180°180° Steps:
  1. Locate the centre of rotation at (2,12, 1) on the grid.
  2. Rotate each point of the blue object 180°180° clockwise around (2,12, 1).
  3. Plot the new points and draw the purple object. Notice: Whenever the angle of rotation is 180°180°, the direction (clockwise or anti-clockwise) does not matter—the result is the same.
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