14.5 Rotation · Unit 14 Position and transformation

1 · Teaching slidesuse ← → keys

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2 · Key words

rotationA turn about a fixed point.

centre of rotationThe point everything turns around.

anticlockwiseThe positive direction, opposite to clock hands.

clockwiseThe direction the hands of a clock go.

quarter turn90 degrees.

half turn180 degrees.

3 · Summary of the sectionrevise from this

A rotation turns a shape about a centre of rotation.
To describe one fully you need three things: the angle, the direction and the centre.
About the origin, 90° anticlockwise: (x, y) → (−y, x).
About the origin, 180°: (x, y) → (−x, −y).
About the origin, 90° clockwise: (x, y) → (y, −x).
For 180° the direction makes no difference.
The centre does not move. Everything else does.
About any other centre, work with the offset from the centre, turn that, then add the centre back on.
The image is congruent, and unlike a reflection the vertices still run the same way round.

PDFPrintable worksheet All 64 questions, space to work PDFWorked answers Full solutions, not just the answer

Video lessons2 videos

Rotations

British corbettmaths

Rotating about a centre, using tracing paper as the model for what the arithmetic does.

Describing Rotations

British corbettmaths

Working backwards: given an object and its image, find the angle, the direction and the centre.

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Rotation