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4MA1/1FR Jun 2018, Question 17: Reflection

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1FR (Foundation) · Calculator · 5 marks

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The question, in short

On a grid, triangle S has vertices (5, 3), (6, 3) and (6, 5). Carry out two transformations of S, then identify the single transformation taking triangle P to triangle Q.

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

Part (a) · 2 marks

Draw the image of S after reflection in the line y = x and name it R.

  1. 1Reflect each vertex of triangle S in the line y = x
  2. 2Original vertices of S: (6,5), (6,3), (5,3)
  3. 3Swap x and y coordinates: (5,6), (3,6), (3,5)
  4. 4Plot and label new triangle R with these vertices

Answer(5,6), (3,6), (3,5)

Part (b) · 1 mark

Draw the image of S after a translation by the vector (−4, −6) and name it T.

  1. 1Vector (−4, −6) means 4 left and 6 down
  2. 2(6, 5) → (2, −1) and (6, 3) → (2, −3)
  3. 3(5, 3) → (1, −3)
  4. 4T has vertices (2,−1), (2,−3), (1,−3)

Answer(2,−1), (2,−3), (1,−3)

Part (c) · 2 marks

State fully the one transformation that maps P onto Q, where P has vertices (1, 2), (2, 2), (1, 4) and Q has vertices (3, 6), (6, 6), (3, 12).

  1. 1P (1, 2) maps to (3, 6) and (2, 2) maps to (6, 6)
  2. 2Each side of Q is 3 times as long: scale factor 3
  3. 3Each Q point is 3 × its P point, so the centre is (0, 0)
  4. 4Enlargement, scale factor 3, centre the origin

AnswerEnlargement Scale factor 3 and centre the origin

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