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Geometry & measures · Transformations

Chapter 1 · 4

The idea

Translations & enlargements

Column vectors as translations, enlargement by a positive, fractional or negative scale factor from a centre, finding the centre and scale factor from a picture, and why lengths scale but angles don't.

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Geometry & measures · Transformations

Translations & enlargements

Column vectors as translations, enlargement by a positive, fractional or negative scale factor from a centre, finding the centre and scale factor from a picture, and why lengths scale but angles don't.

Why it works

Translation: a column vector slide

A translation slides every point by the same column vector.

(ab)means a across (right if positive), b up (up if positive).\begin{pmatrix} a \\ b \end{pmatrix} \quad\text{means } a \text{ across (right if positive), } b \text{ up (up if positive).}

Top number across, bottom number up — always. Writing the pair as coordinates (a,b)(a, b) instead of a column vector loses the mark, and so does swapping the two numbers.

Enlargement scales distance from the centre

For scale factor kk about centre CC, every point PP moves along the ray CPCP to the point kk times as far from CC:

CP′=k×CPCP' = k \times CP

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The rest of the explanation, plus 2 worked examples you step through move by move.

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