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0580/42 Feb/Mar 2021, Question 2: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 10 marks

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The question, in short

Using the grid with triangles A, B and C, describe transformations between triangles, then draw images of A under a translation and a reflection.

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

Part (ai) · 3 marks

Describe fully the single transformation mapping triangle A onto triangle B.

  1. 1Triangle is turned a quarter turn anticlockwise
  2. 2Find the centre with tracing paper or perpendicular bisectors: (−3, 2)
  3. 3Check: (2, 5) → (−6, 7), (6, 5) → (−6, 11), (6, 13) → (−14, 11)
  4. 4Rotation, 90° anticlockwise, centre (−3, 2)

AnswerRotation, 90° anticlockwise, centre (−3, 2)

Part (aii) · 3 marks

Describe fully the single transformation mapping triangle A onto triangle C.

  1. 1C is upside down and half the size, so scale factor −1/2
  2. 2Join (2, 5) to (−4, −4) and (6, 5) to (−6, −4); the lines cross at (−2, −1)
  3. 3Enlargement, scale factor −1/2, centre (−2, −1)

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

Part (b) · 2 marks

Draw the image of triangle A after translation by column vector (−5, −10).

  1. 1Subtract 5 from each x and 10 from each y
  2. 2(2, 5) → (−3, −5), (6, 5) → (1, −5), (6, 13) → (1, 3)
  3. 3Draw the triangle (−3, −5), (1, −5), (1, 3)

AnswerImage at (−3, −5), (1, −5), (1, 3)

Part (c) · 2 marks

Draw the image of triangle A after reflection in the line y = 4.

  1. 1Each point is the same distance on the other side of y = 4: y becomes 8 − y
  2. 2(2, 5) → (2, 3), (6, 5) → (6, 3), (6, 13) → (6, −5)
  3. 3Draw the triangle (2, 3), (6, 3), (6, −5)

AnswerImage at (2, 3), (6, 3), (6, −5)

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Also searched as: 0580/42/F/M/21 · 0580_m21_qp_42 · 0580 m21 42 · question 2.
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