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0580/22 Feb/Mar 2024, Question 15: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 7 marks

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The question, in short

Using three labelled triangles on a coordinate grid, identify transformations linking them and construct a rotated image of one triangle.

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

Part (ai) · 2 marks

State the single transformation taking triangle A to triangle B, giving all defining details.

  1. 1(1, 2) → (−5, 2): mirror line halfway between x = 1 and x = −5
  2. 2(1 + (−5)) ÷ 2 = −2
  3. 3Reflection in the line x = −2

AnswerReflection in x = −2

Part (aii) · 3 marks

State the single transformation taking triangle A to triangle C, giving all defining details.

  1. 1Side (1, 2) to (1, −2) of length 4 maps to (−1, −1) to (−1, −3) of length 2, so scale factor 1/2
  2. 2Lines through corresponding vertices, e.g. (1, 2) to (−1, −1) and (5, −1) to (1, −2.5), meet at (−3, −4)
  3. 3Enlargement, scale factor 1/2, centre (−3, −4)

AnswerEnlargement, scale factor 1/2, centre (−3, −4)

Part (b) · 2 marks

Plot triangle A's image after turning it 90° clockwise around (1, 3).

  1. 1Turn each vertex 90° clockwise about (1, 3)
  2. 2(1, 2) → (0, 3), (1, −2) → (−4, 3), (5, −1) → (−3, −1)
  3. 3Draw the triangle with vertices (0, 3), (−4, 3), (−3, −1)

AnswerImage at (0, 3 ), (−4, 3), (−3, −1)

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