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4024/22 May/Jun 2020, Question 11: Describing Transformations

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 7 marks

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The question, in short

Use the grid with triangles A, B and C to describe a transformation, find a matrix, and draw a combined transformation image.

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

Part (a) · 2 marks

Describe fully the single transformation taking triangle A to triangle B.

  1. 1(3, 2) → (3, −4) and (4, 5) → (4, −7): the mirror line is halfway, y = (2 + (−4))/2 = −1
  2. 2Reflection in the line y = −1

AnswerReflection, y = −1

Part (b) · 2 marks

Find the matrix of the single transformation H mapping triangle A onto triangle C.

  1. 1(3, 2) → (−2, 3), (4, 2) → (−2, 4), (4, 5) → (−5, 4): (x, y) → (−y, x)
  2. 2This is a rotation 90° anticlockwise about (0, 0)
  3. 3Matrix H = (0 −1 / 1 0)

Answer(0 −1 / 1 0)

Part (c) · 3 marks

Given M is reflection in x = 2 and R is 180° rotation about (0, 0), draw and label triangle D where RM(A) = D.

  1. 1Reflect A in x = 2: (3, 2) → (1, 2), (4, 2) → (0, 2), (4, 5) → (0, 5)
  2. 2Rotate 180° about (0, 0): (x, y) → (−x, −y)
  3. 3D has vertices (−1, −2), (0, −2), (0, −5)

AnswerTriangle with vertices (−1, −2), (0, −2), (0, −5)

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