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0580/42 Oct/Nov 2021, Question 4: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 9 marks

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The question, in short

Using the grid with triangles A and B, carry out three transformations on A and identify the single transformation linking A to B.

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

Part (ai) · 2 marks

Plot triangle A moved by the vector (−4, 5) and draw its image.

  1. 1Add (−4, 5) to each vertex: (−1, 1) → (−5, 6), (−1, 3) → (−5, 8), (−2, 2) → (−6, 7)
  2. 2Draw the triangle with vertices (−5, 6), (−5, 8), (−6, 7)

AnswerImage at (−5, 6) (−5, 8) (−6, 7)

Part (aii) · 2 marks

Draw triangle A reflected across the vertical line x = 1.

  1. 1Draw the line x = 1; each point moves to the same distance on the other side: x → 2 − x
  2. 2(−1, 1) → (3, 1), (−1, 3) → (3, 3), (−2, 2) → (4, 2)

AnswerImage at (3, 1) (3, 3) (4, 2)

Part (aiii) · 2 marks

Draw triangle A enlarged by scale factor 2 about the point (−5, −2).

  1. 1From centre (−5, −2), multiply each vector to a vertex by 2
  2. 2(−1, 1): vector (4, 3) → (8, 6), image (3, 4)
  3. 3(−1, 3): vector (4, 5) → (8, 10), image (3, 8)
  4. 4(−2, 2): vector (3, 4) → (6, 8), image (1, 6)

AnswerImage at (3, 4) (3, 8) (1, 6)

Part (b) · 3 marks

State fully the one transformation taking triangle A onto triangle B.

  1. 1Triangle A is given a quarter-turn, so it is a rotation.
  2. 2Use tracing paper to find the centre: (−3, 0).
  3. 3Check: (−1, 1) → (−4, 2), (−1, 3) → (−6, 2), (−2, 2) → (−5, 1)
  4. 4Rotation, 90° anticlockwise, centre (−3, 0)

AnswerRotation 90° anticlockwise, centre (−3, 0)

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Also searched as: 0580/42/O/N/21 · 0580_w21_qp_42 · 0580 w21 42 · question 4.
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