Rotations (Leaving Cert Mathematics): Revision Notes

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 $90°, 180°, or\ 270°$.
• Direction of rotation: This can be clockwise or anti-clockwise.

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 ($0, 0$) or ($2, 1$).
2. Direction of Rotation: This is the degree of rotation, which is usually $90°, 180°$, or $270°$.
3. Angle of Rotation: This is the degree of rotation, which is usually $90°, 180°$, or $270°$.

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

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

• Centre of Rotation: ($0, 0$) - the origin
• Direction of Rotation: Clockwise
• Angle of Rotation: $90°$ Steps:

1. Locate the centre of rotation at ($0, 0$) on the grid.
2. Rotate each point of the blue object $90°$ 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 $270°$ anti-clockwise rotation since both produce the same result.

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

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

• Centre of Rotation: ($2, 1$)
• Direction of Rotation: Clockwise
• Angle of Rotation: $180°$ Steps:

4. Locate the centre of rotation at ($2, 1$) on the grid.
5. Rotate each point of the blue object $180°$ clockwise around ($2, 1$).
6. Plot the new points and draw the purple object. Notice: Whenever the angle of rotation is $180°$, the direction (clockwise or anti-clockwise) does not matter—the result is the same.