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0580/33 Oct/Nov 2021, Question 3: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 12 marks

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The question, in short

Find rotational symmetry orders for two shapes, then describe transformations between triangles A, B, C and perform a reflection and a translation on a grid.

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

Part (a) · 2 marks

State the order of rotational symmetry for the regular octagon and for the cross shape.

  1. 1Regular octagon: order 8
  2. 2Cross shape: order 4

Answer8 and 4

Part (bia) · 3 marks

Describe fully the single transformation mapping triangle A onto triangle B.

  1. 1Lengths double (3 → 6), so scale factor 2
  2. 2Lines through corresponding vertices, e.g. (−3, −5) → (1, −5) and (−3, −2) → (1, 1), meet at (−7, −5)
  3. 3Enlargement, centre (−7, −5), scale factor 2

AnswerEnlargement, centre (−7, −5), scale factor 2

Part (bib) · 3 marks

Describe fully the single transformation mapping triangle A onto triangle C.

  1. 1(x, y) → (−x, −y): (−3, −2) → (3, 2), (−3, −5) → (3, 5), (−1, −5) → (1, 5)
  2. 2Rotation, centre (0, 0), 180°

AnswerRotation, centre (0, 0), 180°

Part (bii) · 2 marks

Reflect triangle C in the line x = −1 on the grid.

  1. 1Reflection in x = −1: (x, y) → (−2 − x, y)
  2. 2(1, 5) → (−3, 5), (3, 5) → (−5, 5), (3, 2) → (−5, 2)
  3. 3Draw the triangle (−3, 5), (−5, 5), (−5, 2)

AnswerTriangle at (−3, 5), (−5, 5), (−5, 2)

Part (biii) · 2 marks

Translate triangle C by the column vector (5, −1) on the grid.

  1. 1Add 5 to x and subtract 1 from y: (1, 5) → (6, 4), (3, 5) → (8, 4), (3, 2) → (8, 1)
  2. 2Draw the triangle (6, 4), (8, 4), (8, 1)

AnswerTriangle at (6, 4), (8, 4), (8, 1)

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Also searched as: 0580/33/O/N/21 · 0580_w21_qp_33 · 0580 w21 33 · question 3.
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