The Four Transformations (Edexcel GCSE Maths): Flashcards

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The four transformations
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Four main transformations in geometry

Translation, rotation, reflection, enlargement

Translation effect on shape

Moves shape without changing size, shape, or orientation

Translation vector form

(xy)\begin{pmatrix} x \\ y \end{pmatrix} (x horiz., y vert.)

Positive xx in translation vector means

Rightward movement

Negative yy in translation vector means

Downward movement

Three elements needed to describe rotation

Angle, direction, centre of rotation

180° rotation direction property

Direction doesn't matter (same result either way)

To describe a reflection, you need

The equation of the mirror line

Two elements needed for enlargement

Scale factor and centre of enlargement

Scale factor formula

new lengthold length\frac{\text{new length}}{\text{old length}}

Scale factor > 1 effect

Shape gets bigger

Negative scale factor effect

Shape appears on opposite side of centre

Congruent vs similar shapes

Congruent: same size & shape; Similar: same shape, diff size

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