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0580/42 Feb/Mar 2023, Question 4: Reflection

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 12 marks

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The question, in short

Use a grid with triangle T at (1, 1), (3, 1), (3, 2) to carry out transformations and identify a single mapping between two given images.

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

Part (ai) · 2 marks

Scale triangle T by 3 from centre (0, 2) and draw the enlarged triangle.

  1. 1Multiply each vertex's distance from (0, 2) by 3
  2. 2(1, 1) → (0 + 3 × 1, 2 + 3 × (−1)) = (3, −1)
  3. 3(3, 1) → (9, −1)
  4. 4(3, 2) → (9, 2)
  5. 5Draw the triangle (3, −1), (9, −1), (9, 2)

AnswerTriangle at (3, −1), (9, −1), (9, 2)

Part (aiia) · 2 marks

Turn triangle T 90° clockwise about (4, 2) and mark the result P.

  1. 1Turn each vertex 90° clockwise about (4, 2)
  2. 2(1, 1) → (3, 5), (3, 1) → (3, 3), (3, 2) → (4, 3)
  3. 3Draw triangle P at (3, 3), (4, 3), (3, 5)

AnswerTriangle at (3, 3), (4, 3), (3, 5)

Part (aiib) · 3 marks

Mirror triangle T in the line x + y = 6 and mark the result Q.

  1. 1Draw the line x + y = 6, through (0, 6) and (6, 0)
  2. 2Reflection in x + y = 6 sends (x, y) to (6 − y, 6 − x)
  3. 3(1, 1) → (5, 5), (3, 1) → (5, 3), (3, 2) → (4, 3)
  4. 4Draw triangle Q at (4, 3), (5, 3), (5, 5)

AnswerTriangle at (4, 3), (5, 3), (5, 5)

Part (aiic) · 2 marks

Given P at (3, 3), (4, 3), (3, 5) and Q at (4, 3), (5, 3), (5, 5), state the one transformation taking P to Q.

  1. 1P: (3, 3), (4, 3), (3, 5); Q: (5, 3), (4, 3), (5, 5)
  2. 2(4, 3) is fixed and each other point is the same distance either side of x = 4
  3. 3Reflection in the line x = 4

AnswerReflection, x = 4

Part (b) · 3 marks

In triangle OHK with position vectors a for H and b for K, Z splits HK in ratio 2 : 5; find Z's position vector in a and b.

  1. 1HK = −a + b
  2. 2HZ = 2/7 HK = 2/7(b − a)
  3. 3OZ = a + 2/7(b − a)
  4. 4= 5/7 a + 2/7 b

Answer5/7 a + 2/7 b

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Also searched as: 0580/42/F/M/23 · 0580_m23_qp_42 · 0580 m23 42 · question 4.
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