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0580/42 Oct/Nov 2022, Question 4: Describing Transformations

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

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The question, in short

Using coordinates of shapes A, B, C and D on a grid, identify single transformations mapping A to each shape, then draw A's reflection in y = x + 8.

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Part (ai) · 2 marks

Describe the single transformation taking shape A onto shape B.

  1. 1(−5, 4) → (2, −4): 7 right and 8 down
  2. 2Translation by column vector (7, −8)

AnswerTranslation, column vector (7, −8)

Part (aii) · 3 marks

Describe the single transformation taking shape A onto shape C.

  1. 1A is turned through 90° anticlockwise, e.g. (−5, 4) → (4, 3), (−5, 6) → (2, 3)
  2. 2Both points are the same distance from (0, 8) before and after
  3. 3Rotation, 90° anticlockwise, centre (0, 8)

AnswerRotation, 90° anticlockwise, centre (0, 8)

Part (aiii) · 3 marks

Describe the single transformation taking shape A onto shape D.

  1. 1D is half the size of A, same way up
  2. 2Lines through (−5, 4) → (−3, 0) and (−5, 6) → (−3, 1) meet at (−1, −4)
  3. 3Enlargement, scale factor 1/2, centre (−1, −4)

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

Part (b) · 2 marks

Draw the image of shape A after reflection in the line y = x + 8.

  1. 1Draw the line y = x + 8 (through (−8, 0) and (0, 8))
  2. 2Reflect each vertex: (x, y) → (y − 8, x + 8)
  3. 3Image at (−4, 4), (−3, 4), (−2, 5), (−2, 3), (−4, 3)

AnswerImage at (−4, 4), (−3, 4), (−2, 5), (−2, 3), (−4, 3)

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Also searched as: 0580/42/O/N/22 · 0580_w22_qp_42 · 0580 w22 42 · question 4.
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