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0580/31 May/Jun 2022, Question 5: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 16 marks

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The question, in short

Use grids and a rhombus diagram to read coordinates, plot points, mark an isosceles triangle, state symmetry, and describe or draw transformations of triangles.

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

Part (ai) · 1 mark

State the coordinates of point A shown on the grid.

  1. 1Read across then up: A = (3, 1)

Answer(3, 1)

Part (aii) · 1 mark

Plot point B at (−1, 3) on the grid.

  1. 1From the origin go 1 left and 3 up: plot B at (−1, 3)

AnswerCorrect point plotted

Part (aiii) · 1 mark

Mark a whole-number point C so triangle ABC is isosceles.

  1. 1e.g. C = (0, 0): CA = √(3² + 1²) = √10 and CB = √(1² + 3²) = √10
  2. 2CA = CB, so plot C at (0, 0) and triangle ABC is isosceles

AnswerC plotted such that ABC is isosceles

Part (bi) · 1 mark

State the order of rotational symmetry of the rhombus.

  1. 1The rhombus looks the same twice in a full turn: order 2

Answer2

Part (bii) · 2 marks

Draw all lines of symmetry on the rhombus diagram.

  1. 1Draw both diagonals of the rhombus as ruled lines
  2. 2These are the only 2 lines of symmetry

Answer2 correct lines and no extras

Part (ci) · 3 marks

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

  1. 1B's sides are twice as long as A's, and both have the vertex (2, 1)
  2. 2Enlargement, centre (2, 1), scale factor 2

AnswerEnlargement, centre (2, 1), scale factor 2

Part (cii) · 3 marks

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

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

AnswerRotation, centre (0, 0), 180°

Part (ciiia) · 2 marks

Draw triangle A's image after translation by vector (−5, 3).

  1. 1Move each vertex 5 left and 3 up
  2. 2(2, 1) → (−3, 4), (5, 1) → (0, 4), (2, 3) → (−3, 6)
  3. 3Draw the triangle at (−3, 4), (0, 4), (−3, 6)

AnswerTriangle at (−3, 4), (0, 4), (−3, 6)

Part (ciiib) · 2 marks

Draw triangle A's image after reflection in the line y = −2.

  1. 1y = 1 is 3 above y = −2, so its image is 3 below: y = −5; y = 3 → y = −7
  2. 2Draw the triangle at (2, −5), (5, −5), (2, −7)

AnswerTriangle at (2, −5), (5, −5), (2, −7)

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Also searched as: 0580/31/M/J/22 · 0580_s22_qp_31 · 0580 s22 31 · question 5.
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