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