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0580/41 Oct/Nov 2021, Question 7: Reflection

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 11 marks

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The question, in short

Grid transformations: enlarge and reflect shape A, identify the single transformation mapping A to B, then use vectors p and q in trapezium OABC to find M's position vector.

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

Part (aia) · 2 marks

Draw shape A enlarged by scale factor 2 about centre (0, 1).

  1. 1From (0, 1), double each distance: (−2, 4) → (−4, 7), (0, 4) → (0, 7)
  2. 2(−1, 1) → (−2, 1), (−2, 1) → (−4, 1)
  3. 3Draw the shape (−2, 1), (−4, 1), (−4, 7), (0, 7)

AnswerShape at (−2, 1), (−4, 1), (−4, 7), (0, 7)

Part (aib) · 3 marks

Draw shape A reflected in the line y = x − 1.

  1. 1Reflection in y = x − 1: (x, y) → (y + 1, x − 1)
  2. 2(−2, 4) → (5, −3), (0, 4) → (5, −1), (−1, 1) → (2, −2), (−2, 1) → (2, −3)
  3. 3Draw the shape (2, −2), (2, −3), (5, −1), (5, −3)

AnswerShape at (2, −2), (2, −3), (5, −1), (5, −3)

Part (aii) · 3 marks

State fully the one transformation taking shape A onto shape B.

  1. 1(x, y) → (−y, x): (−2, 4) → (−4, −2), (0, 4) → (−4, 0), (−1, 1) → (−1, −1)
  2. 2Rotation, 90° anticlockwise, centre (0, 0)

AnswerRotation, 90° anticlockwise, centre (0, 0)

Part (b) · 3 marks

With OA = p, OC = q, OA = 2CB and M the midpoint of AB, find M's position vector in p and q, simplified.

  1. 1CB = 1/2 p
  2. 2AB = −p + q + 1/2 p = q − 1/2 p
  3. 3OM = p + 1/2(q − 1/2 p)
  4. 4OM = 3/4 p + 1/2 q

Answer3/4 p + 1/2 q or 1/4(3p + 2q) or (3p + 2q)/4

Stuck on a step? Read the free lesson: Reflection

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Also searched as: 0580/41/O/N/21 · 0580_w21_qp_41 · 0580 w21 41 · question 7.
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