Geometry & MeasuresTopic Summary

Knowledge Organiser: Enlargements

Part of Transformations · GCSE GCSE Mathematics revision

This topic summary covers Knowledge Organiser: Enlargements within Transformations for GCSE Mathematics. Revise Transformations in Geometry & Measures for GCSE Mathematics with 16 exam-style questions and 5 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 6 of 6 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 6 of 6

Practice

16 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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Keep building this topic

Read this section alongside the surrounding pages in Transformations. That gives you the full topic sequence instead of a single isolated revision point.

Practice Questions for Transformations

A translation is described by the vector (3, −2). What does this mean?

  • A. Move 3 units down and 2 units right
  • B. Move 3 units right and 2 units down
  • C. Move 3 units up and 2 units left
  • D. Move 3 units left and 2 units up
1 markfoundation

Shape A is mapped to shape B by a translation. Describe fully what information is needed to describe a translation.

2 marksstandard

Quick Recall Flashcards

Reflection
State the MIRROR LINE (equation). Shape flips over. Points and images are equidistant from mirror line.
Rotation
State CENTRE, ANGLE, and DIRECTION (CW/ACW). Shape turns around fixed point. 180° is same CW or ACW.

16 questions on Transformations — practise free

Instant marking, adaptive difficulty, and 5 spaced repetition flashcards. Free until your GCSEs.

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