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0580/42 May/Jun 2022, Question 5: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 11 marks

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The question, in short

Rectangle symmetry lines, then use the grid with triangles A, B and C to identify transformations and draw two images of A.

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

Part (a) · 2 marks

Draw every line of symmetry for the given rectangle.

  1. 1Draw the vertical line through the midpoints of the top and bottom sides
  2. 2Draw the horizontal line through the midpoints of the two shorter sides
  3. 3A rectangle has exactly 2 lines of symmetry (not the diagonals)

AnswerCorrect lines drawn

Part (bia) · 2 marks

Give the full single transformation taking triangle A to triangle B.

  1. 1(−5, −2) → (−6, 2): 1 left and 4 up
  2. 2Translation by column vector (−1, 4)

AnswerTranslation column vector (−1, 4)

Part (bib) · 3 marks

Give the full single transformation taking triangle A to triangle C.

  1. 1(−5, −2) → (5, −6), (−2, −2) → (5, −3), (−2, −1) → (4, −3)
  2. 2Check centre (2, 1): (−2, −2) − (2, 1) = (−4, −3), rotated 90° anticlockwise gives (3, −4), and (2, 1) + (3, −4) = (5, −3)
  3. 3Rotation, 90° anticlockwise, centre (2, 1)

AnswerRotation, 90° anticlockwise, centre (2, 1)

Part (biia) · 2 marks

Plot triangle A reflected across the line y = 2.

  1. 1Reflection in y = 2: (x, y) → (x, 4 − y)
  2. 2(−5, −2) → (−5, 6), (−2, −2) → (−2, 6), (−2, −1) → (−2, 5)
  3. 3Draw the triangle at (−5, 6), (−2, 6), (−2, 5)

AnswerTriangle at (−5, 6), (−2, 6), (−2, 5)

Part (biib) · 2 marks

Plot triangle A enlarged by scale factor −2 about centre (−1, 1).

  1. 1Image = centre − 2 × (point − centre), centre (−1, 1)
  2. 2(−5, −2): (−4, −3) → (8, 6), image (7, 7)
  3. 3(−2, −2): (−1, −3) → (2, 6), image (1, 7); (−2, −1): (−1, −2) → (2, 4), image (1, 5)
  4. 4Draw the triangle at (1, 5), (1, 7), (7, 7)

AnswerTriangle at (1, 5), (1, 7), (7, 7)

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Also searched as: 0580/42/M/J/22 · 0580_s22_qp_42 · 0580 s22 42 · question 5.
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