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0580/21 May/Jun 2021, Question 10: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 8 marks

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The question, in short

Using the grid with triangles A, B and C, identify single transformations mapping A onto B and A onto C, then draw A's image after a given translation.

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 that maps triangle A onto triangle B.

  1. 1The triangle is turned, so the transformation is a rotation.
  2. 2Rotating A 90° anticlockwise about (0, −1): (−6, −3) → (2, −7), (−6, −9) → (8, −7), (−3, −9) → (8, −4)
  3. 3Rotation, 90° anticlockwise, centre (0, −1)

AnswerRotation, 90° anticlockwise, centre (0, −1)

Part (aii) · 3 marks

Describe fully the single transformation that maps triangle A onto triangle C.

  1. 1C is smaller than A: side 2 against side 6, so scale factor 6 → 2 = 1/3
  2. 2Lines joining matching vertices, e.g. (−6, −3) to (2, 3) and (−3, −9) to (3, 1), meet at (6, 6)
  3. 3Enlargement, scale factor 1/3, centre (6, 6)

AnswerEnlargement, scale factor 1/3, centre (6, 6)

Part (b) · 2 marks

Draw the image of triangle A after translation by the column vector (2, 10).

  1. 1Add 2 to each x-coordinate and 10 to each y-coordinate.
  2. 2(−6, −3) → (−4, 7), (−6, −9) → (−4, 1), (−3, −9) → (−1, 1)
  3. 3Draw the triangle with vertices (−4, 7), (−4, 1), (−1, 1)

AnswerTriangle at (−4, 7), (−4, 1), (−1, 1)

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