Transformations (Copy)

Cheat Sheet: Transformations (IGCSE Mathematics 0580 – CORE)
Topic: Reflection, Rotation, Enlargement, Translation

1. Reflection

• Reflect a shape in a vertical (x = constant) or horizontal (y = constant) line.
• Key facts:
  • Each point and its image are the same distance from the mirror line.
  • Reflection over x-axis: (x, y) → (x, –y)
  • Reflection over y-axis: (x, y) → (–x, y)
• Use a ruler to measure and draw accurately.

2. Rotation

• Rotate a shape about a point (origin, vertex, or midpoint) through multiples of 90° (90°, 180°, 270°).
• Key facts:
  • Rotation is anticlockwise unless stated otherwise (if direction is not specified, assume anticlockwise).
  • Common rotations about the origin:
    • 90° anticlockwise: (x, y) → (–y, x)
    • 180°: (x, y) → (–x, –y)
    • 270° anticlockwise: (x, y) → (y, –x)
• Use tracing paper if allowed to check.

3. Enlargement

• Enlarge a shape from a centre using a scale factor.
• Key facts:
  • If scale factor > 1 → shape gets bigger.
  • If 0 < scale factor < 1 → shape gets smaller.
  • Lines from the centre of enlargement through each point are extended or shortened by the scale factor.
  • Enlargement preserves shape angles and proportions.
• Only positive and fractional scale factors are used.

4. Translation

• Move (slide) a shape without turning it.
• Key facts:
  • Translation is described by a vector written as:

    (xy)begin{pmatrix} x \ y end{pmatrix}

  • x = movement right (+) or left (–)
  • y = movement up (+) or down (–)
  • Example:

    (3−2)begin{pmatrix} 3 \ -2 end{pmatrix}means 3 units right and 2 units down.

5. Important Tips

• Use a ruler for all straight lines.
• Check distances carefully for reflections.
• Mark centre of rotation or enlargement clearly if needed.
• Follow the vector exactly for translations — do not guess.

This cheat sheet fully covers CORE-level methods for recognising, describing, and drawing reflections, rotations, enlargements, and translations (no combinations).