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0580/32 Feb/Mar 2021, Question 3: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 12 marks

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The question, in short

Use the grid diagram with triangles A, B and C to measure an angle, justify congruence, describe transformations, and draw translated and reflected images of A.

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

Part (a) · 1 mark

Measure angle w at the marked vertex of triangle B.

  1. 1Place the protractor at the vertex (−3, 7) and measure between the two sides
  2. 2w = 72°

Answer72 (accept 70 to 74)

Part (b) · 1 mark

Give a reason why triangles B and C are congruent.

  1. 1B and C have exactly the same shape and size (C is B rotated through 180°), so they are congruent

AnswerSame shape and size: C is B rotated through 180°

Part (ci) · 3 marks

Fully describe the single transformation taking triangle A to triangle B.

  1. 1A has base 3 units ((−4, 3) to (−1, 3)); B has base 9 units, so scale factor 9 ÷ 3 = 3
  2. 2Join corresponding vertices, e.g. (−4, 3) to (−6, 1) and (−3, 5) to (−3, 7); the lines meet at (−3, 4)
  3. 3Enlargement, centre (−3, 4), scale factor 3

AnswerEnlargement, centre (−3, 4), scale factor 3

Part (cii) · 3 marks

Fully describe the single transformation taking triangle B to triangle C.

  1. 1Each vertex (x, y) of B maps to (−x, −y) in C, e.g. (−3, 7) → (3, −7)
  2. 2Rotation, centre (0, 0), 180°

AnswerRotation, centre (0, 0), 180°

Part (di) · 2 marks

Draw shape A's image after translation by vector (7, −1).

  1. 1Add 7 to each x and subtract 1 from each y
  2. 2(−4, 3) → (3, 2), (−3, 5) → (4, 4), (−1, 3) → (6, 2)
  3. 3Draw the triangle (3, 2), (4, 4), (6, 2)

AnswerCorrect translation: (3, 2), (4, 4), (6, 2)

Part (dii) · 2 marks

Draw shape A's image after reflection in the line y = −1.

  1. 1Each point is the same distance below y = −1 as it is above: y becomes −2 − y
  2. 2(−4, 3) → (−4, −5), (−3, 5) → (−3, −7), (−1, 3) → (−1, −5)
  3. 3Draw the triangle (−1, −5), (−3, −7), (−4, −5)

AnswerCorrect reflection: (−1, −5), (−3, −7), (−4, −5)

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Also searched as: 0580/32/F/M/21 · 0580_m21_qp_32 · 0580 m21 32 · question 3.
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