Flashcards · Maths · Transformations and Similarity
Rotations
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What is a rotation?
A turn of a shape through an angle about a fixed point.
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What is the centre of rotation?
The point that stays fixed when a shape is rotated.
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What details describe a rotation?
The centre, the angle and the direction.
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What are the common angles of rotation in a non-calculator exam?
\(90^\circ\), \(180^\circ\) and \(270^\circ\).
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Why is no direction needed for a \(180^\circ\) rotation?
Both directions give the same result.
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Where does \((x, y)\) go in a \(180^\circ\) rotation about the origin?
\((-x, -y)\).
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Where does \((x, y)\) go in a \(90^\circ\) clockwise rotation about the origin?
\((y, -x)\).
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Where does \((x, y)\) go in a \(90^\circ\) anticlockwise rotation about the origin?
\((-y, x)\).
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How far is each point from the centre after a rotation?
The same distance as before.
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How do you find the centre of a rotation?
Find where the perpendicular bisectors of the lines joining points to their images cross.
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How can tracing paper help?
Put the pencil on the centre and turn the paper to check the image.
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How do you find the centre of a \(180^\circ\) rotation?
It is the midpoint of any point and its image.
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Is the image of a rotation the same size as the object?
Yes, it is congruent.
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What is a quarter turn?
A rotation of \(90^\circ\).
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What is a half turn?
A rotation of \(180^\circ\).
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Which way is clockwise?
The same way as the hands of a clock.