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4024/12 Oct/Nov 2020, Question 19: Describing Transformations

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 6 marks

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The question, in short

Using the grid with triangles A and B and point P at (−2, 2), identify the single transformation taking A to B, give its matrix, then draw triangle C from an enlargement of A about P with scale factor −1/2.

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Part (ai) · 2 marks

State fully the one transformation that carries triangle A onto triangle B.

  1. 1Each point (x, y) of A maps to (x, −y) in B, e.g. (2, 4) → (2, −4)
  2. 2Reflection in the x-axis (y = 0)

AnswerReflection in the x-axis (y = 0)

Part (aii) · 2 marks

Give the matrix for the transformation found in part (ai).

  1. 1(1, 0) → (1, 0) and (0, 1) → (0, −1)
  2. 2Matrix = (1 0 / 0 −1)

Answer(1 0 / 0 −1)

Part (b) · 2 marks

Draw and label triangle C, the image of A under enlargement centre P (−2, 2), scale factor −1/2.

  1. 1Vectors from P to A's vertices: (4, 0), (4, 2), (8, 0)
  2. 2Multiply by −1/2: (−2, 0), (−2, −1), (−4, 0)
  3. 3Add to P (−2, 2): C has vertices (−4, 2), (−4, 1), (−6, 2)

AnswerTriangle C at (−4, 1), (−4, 2), (−6, 2)

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Also searched as: 4024/12/O/N/20 · 4024_w20_qp_12 · 4024 w20 12 · question 19.
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