Rotation
Turning a shape around a fixed point, called the centre of rotation, by a certain angle and direction.
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Analogy
Like the hands of a clock turning round the middle.
Example
90 degrees anticlockwiseRule: (x, y) becomes (-y, x)New point (-1, 2)
In practice
Windmills and fairground wheels turn about a centre.
Practice
Flashcards
- What three things describe a rotation?Angle, direction and centre.
Interview questions
- Describe fully the transformation that takes point (2, 1) to (-1, 2).
- It is a rotation
- The angle is 90 degrees anticlockwise
- The centre is the origin
- Rule (x, y) becomes (-y, x)
Questions people ask
What three things describe a rotation?
You need the angle, the direction (clockwise or anticlockwise) and the centre of rotation. Missing any one of these means the description is incomplete. A rotation of 180 degrees does not need a direction as both ways end up in the same place.
Does rotation change the size of a shape?
No. A rotation keeps the shape the same size, with the same side lengths and angles. Only its position and orientation change. That makes the original and the rotated shape congruent. This is why rotations, reflections and translations are all called congruent transformations. Only enlargement changes size.