Exercise 1 — Cambridge IGCSE 0580 Jun 2025 Paper 42 Q25
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Cambridge IGCSE·Mathematics 0580·Extended
Constructions
Key knowledge — Transformations
Formulas & equations
Translation by vector (a, b): every point moves +a in x, +b in yEnlargement: image length = scale factor × object lengthArea after enlargement = k² × original areaRotation matrix 90° anticlockwise: (x,y) → (−y, x)Reflection in y = x: (x,y) → (y, x)Reflection in y = −x: (x,y) → (−y, −x)
Key facts & rules
- A translation is described by a vector — no angle or centre needed.
- A rotation needs: angle, direction (CW/CCW), and centre of rotation.
- A reflection needs: the equation of the mirror line.
- An enlargement needs: scale factor and centre of enlargement.
- For a negative scale factor: the image is on the opposite side of the centre.
- Invariant points stay fixed under a transformation.
- Combined transformations: apply right-to-left (T₁T₂ means do T₂ first).
IGCSE Transformations — Constructions Practice Extended
2 Cambridge IGCSE 0580 questions on constructions at the Extended tier — each with its full mark scheme.
How to approach constructions — open the study guide
Constructions for transformations (Extended)
Use ruler and compass to construct images: most often enlargements from a centre.
Practice exercises
Exercise 2 — Cambridge IGCSE 0580 Nov 2024 Paper 22 Q22
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