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Edexcel GCSE Maths

Transformations: translation, rotation, reflection and enlargement — Edexcel GCSE Maths revision

Free revision notes, key terms, common exam traps and 5 practice questions with answers. About 6 minutes to read.

Translation and vectors

  • A translation moves every point by a column vector (x, y): top number is left/right, bottom is up/down.
  • Negative x moves left, negative y moves down.
  • Shape size and orientation never change under a translation.

Reflection and rotation

  • Reflect in a line by keeping the perpendicular distance from every point the same on the other side.
  • Common lines: x = 0 (y-axis), y = 0 (x-axis), y = x, y = -x.
  • A rotation needs a centre, an angle, and a direction (clockwise or anticlockwise) to be fully described.
  • Rotating 180° gives the same image whichever direction you go.

Key terms

Translation
A slide described by a column vector, no change of size or orientation.
Rotation
A turn about a fixed centre through a given angle and direction.
Reflection
A flip over a mirror line, producing a mirror image.
Enlargement
A resize from a centre by a scale factor.
Centre of enlargement
The fixed point from which distances are scaled.
Scale factor
The number each length is multiplied by in an enlargement.

Common exam traps

  • Forgetting to state direction (clockwise/anticlockwise) for a rotation.
  • Giving a rotation without a centre.
  • Mixing up the x and y values in a column vector.

Practice questions with answers

  1. 1. Translate the point (2, 3) by the vector (4, -1). Give the new coordinates.

    Answer: (6, 2)

    x: 2+4=6. y: 3+(-1)=2. New point (6, 2).

  2. 2. Reflect the point (3, 5) in the y-axis (x = 0).

    • • (-3, 5)
    • • (3, -5)
    • • (-3, -5)
    • • (5, 3)

    Answer: (-3, 5)

    Reflecting in the y-axis negates the x-coordinate: (3,5) → (-3,5).

  3. 3. Reflect the point (4, -2) in the x-axis (y = 0).

    • • (4, 2)
    • • (-4, -2)
    • • (-4, 2)
    • • (2, -4)

    Answer: (4, 2)

    Reflecting in the x-axis negates the y-coordinate: (4,-2) → (4,2).

  4. 4. Reflect the point (2, 7) in the line y = x.

    Answer: (7, 2)

    Reflecting in y = x swaps the coordinates: (2,7) → (7,2).

  5. 5. A shape is rotated 180° about the origin. What is the image of the point (5, -3)?

    Answer: (-5, 3)

    A 180° rotation about the origin negates both coordinates: (5,-3) → (-5,3).

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