G7GeometryFoundation & Higher

Transformations

A transformation moves or resizes a shape. There are four to know: translation (slide), reflection (flip), rotation (turn) and enlargement (resize). Each needs specific information to describe it fully.

45 min Video by Maths Genie AQA GCSE Maths

Enlargement (Transformations of Shapes)Watch the walkthrough, then read the notes below.

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What you'll learn

Translate a shape by a vector
Reflect a shape in a mirror line
Rotate a shape about a point
Enlarge a shape by a scale factor

The four transformations

$Translation$ : slide by a column vector. $Reflection$ : flip in a mirror line (give the line equation). $Rotation$ : turn about a centre (give angle, direction, centre). $Enlargement$ : resize by a scale factor from a centre.

(3 - 2) = 3 right, 2 down

A translation column vector.

Describing fully

Exam questions often say “describe fully”. You must name the transformation AND give all its details — miss one and you lose marks. Enlargement with a fractional scale factor makes the shape smaller.

1Each length multiplies by the scale factor.

2So every side becomes 3 times longer.

AnswerAll sides become 3× longer.

Tip — To “describe fully”: translation needs a vector; reflection a line; rotation angle+direction+centre; enlargement scale factor+centre.

Remember these

translation: column vector

Slide (no turning or resizing).

enlargement: scale factor + centre

Resize from a point.

Watch out for these

Describing a rotation with only the angle.

Give the angle, the direction, AND the centre of rotation.

Thinking enlargement always makes shapes bigger.

A scale factor between 0 and 1 makes the shape smaller.

Key takeaways

Four transformations: translation, reflection, rotation, enlargement.
Translation = vector; reflection = mirror line; rotation = angle+direction+centre; enlargement = scale factor+centre.
“Describe fully” means give every detail.

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