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0580/32 Oct/Nov 2022, Question 6: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 10 marks

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The question, in short

Using the grid and four flags F, A, B, C, describe the single transformations mapping F onto A, B and C, then draw F'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 taking flag F onto flag A.

  1. 1Square side 1 → 3, so scale factor 3
  2. 2Lines through (−2, 2) and (4, 4), and through (−2, 1) and (4, 1), meet at (−5, 1)
  3. 3Enlargement, centre (−5, 1), scale factor 3

AnswerEnlargement, centre (−5, 1), scale factor 3

Part (aii) · 3 marks

Describe fully the single transformation taking flag F onto flag B.

  1. 1(x, y) → (−y, x): (−2, 2) → (−2, −2), (−1, 3) → (−3, −1), (−2, 1) → (−1, −2)
  2. 2Rotation, centre (0, 0), 90° anticlockwise

AnswerRotation, centre (0, 0), 90° anti-clockwise

Part (aiii) · 2 marks

Describe fully the single transformation taking flag F onto flag C.

  1. 1(−2, 1) → (−2, −5) and (−2, 3) → (−2, −7): the mirror line is halfway, y = −2
  2. 2Reflection in y = −2

AnswerReflection in y = −2

Part (b) · 2 marks

Draw on the grid the image of flag F after translation by the vector (3, −4).

  1. 1Move every point 3 right and 4 down
  2. 2Pole from (1, −3) to (1, −1); flag square with corners (1, −2), (2, −2), (2, −1), (1, −1), with both diagonals

AnswerFlag with outline at (1, −3), (1, −2), (1, −1), (2, −1) and (2, −2)

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Also searched as: 0580/32/O/N/22 · 0580_w22_qp_32 · 0580 w22 32 · question 6.
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