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0580/41 May/Jun 2025, Question 4: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 7 marks

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The question, in short

Using coordinates of shapes A, B and C on a grid, identify transformations between shapes and draw a reflected image of A.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (ai) · 2 marks

Find the single transformation taking shape A to shape B, giving its full description.

  1. 1(−6, 6) on A maps to (2, 3) on B: 8 right, 3 down
  2. 2Translation by column vector (8, −3)

AnswerTranslation column vector (8, −3)

Part (aii) · 3 marks

Find the single transformation taking shape A to shape C, giving its full description.

  1. 1Shape C is the same size as A, but turned a quarter turn.
  2. 2A 90° anticlockwise turn about (0, 0) sends (x, y) to (−y, x).
  3. 3Test corners: (−6, 6) → (−6, −6) and (−5, 2) → (−2, −5), both on C.
  4. 4Rotation 90° anticlockwise centre (0, 0)

AnswerRotation 90° anticlockwise centre (0, 0)

Part (b) · 2 marks

Draw shape A's image after reflection in the line x = −2.

  1. 1Reflect in x = −2: new x = −4 − x, y unchanged
  2. 2(−6, 6) → (2, 6), (−4, 6) → (0, 6), (−4, 5) → (0, 5)
  3. 3(−5, 5) → (1, 5), (−5, 2) → (1, 2), (−6, 2) → (2, 2)
  4. 4Draw the image with vertices (0, 5), (0, 6), (2, 6), (2, 2), (1, 2), (1, 5)

AnswerImage drawn at (0, 5) (0, 6) (2, 6) (2, 2) (1, 2) (1, 5)

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Also searched as: 0580/41/M/J/25 · 0580_s25_qp_41 · 0580 s25 41 · question 4.
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