Knowledge Organiser: Enlargements
Part of Transformations: Enlargements · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Enlargements within Transformations: Enlargements for GCSE Mathematics. Revise Transformations: Enlargements in Geometry & Measures for GCSE Mathematics with 15 exam-style questions and 5 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 7 of 7 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 7 of 7
Practice
15 questions
Recall
5 flashcards
Knowledge Organiser: Enlargements
Key Terms
- Scale factor (SF): The multiplier applied to every length
- Centre of enlargement: The fixed point from which the shape is scaled
- Fractional scale factor: 0 < SF < 1 makes the shape smaller
- Negative scale factor: Enlarges AND inverts through the centre
Must-Know Facts
- Enlargement is the ONLY transformation that changes size
- Always state: centre of enlargement AND scale factor
- SF > 1: shape gets bigger; SF < 1 (but > 0): shape gets smaller
- Area scale factor = SF²; Volume scale factor = SF³
- Negative SF: shape is on the opposite side of the centre, inverted
Key Methods
- From centre, multiply distance to each vertex by SF
- Scale factor = image length ÷ object length
- Area SF = SF²; length SF = √(area ratio)
- Volume SF = SF³; length SF = ∛(volume ratio)
Key Formulas
- Scale factor (SF) = image length ÷ object length
- New coordinate from centre (cx, cy): image = centre + SF × (vertex − centre)
- Area ratio = SF²; Volume ratio = SF³
- Negative SF: image appears on the opposite side of the centre, inverted
Common Mistakes
- Enlarging from wrong point: All distances are measured from the CENTRE of enlargement — not from the origin
- Fractional SF makes shape larger: SF between 0 and 1 makes the shape SMALLER — only SF > 1 makes it larger
- Negative SF: Negative SF reflects through the centre AND scales — the image is on the opposite side
- Area and volume scale: If lengths scale by SF, areas scale by SF² and volumes by SF³ — not the same factor
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Practice Questions for Transformations: Enlargements
Which of the following statements correctly describes an enlargement?
Triangle P has vertices at (2, 1), (6, 1) and (2, 5). Triangle Q has vertices at (4, 2), (12, 2) and (4, 10). Describe fully the single transformation that maps triangle P onto triangle Q.
Quick Recall Flashcards
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