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0580/32 May/Jun 2023, Question 6: Quadrilateral Properties

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 13 marks

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The question, in short

For two quadrilaterals, identify symmetry lines and their mathematical names; then use a grid with triangles A, B and C to describe transformations and perform a reflection.

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

Part (ai) · 3 marks

Draw every line of symmetry on quadrilateral (i) and state its mathematical name.

  1. 1All four sides are equal
  2. 2Draw both diagonals: each one is a line of symmetry
  3. 3Rhombus

AnswerTwo correct diagonals drawn (lines of symmetry); rhombus

Part (aii) · 2 marks

Draw every line of symmetry on quadrilateral (ii) and state its mathematical name.

  1. 1Two pairs of equal adjacent sides
  2. 2Draw the one diagonal through the vertices between the equal sides: this is the only line of symmetry
  3. 3Kite

Answer1 correct diagonal drawn (line of symmetry); kite

Part (bia) · 3 marks

Give the single transformation taking triangle A to triangle B, fully described.

  1. 1Side (1, 2) to (4, 2) has length 3; image side (−5, −6) to (4, −6) has length 9
  2. 2Scale factor = 9 ÷ 3 = 3
  3. 3Lines through (1, 2) and (−5, −6), and through (4, 2) and (4, −6), meet at (4, 6)
  4. 4Enlargement, scale factor 3, centre (4, 6)

AnswerEnlargement, scale factor 3, centre (4, 6)

Part (bib) · 3 marks

Give the single transformation taking triangle A to triangle C, fully described.

  1. 1(1, 2) → (2, −1), (1, 4) → (4, −1), (4, 2) → (2, −4)
  2. 2Each point (x, y) → (y, −x)
  3. 3Rotation, 90° clockwise, centre (0, 0)

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

Part (bii) · 2 marks

Draw the image of triangle A after reflection in the line x = −1.

  1. 1Draw the line x = −1; each point keeps its y and goes the same distance to the other side
  2. 2(1, 2) → (−3, 2), (1, 4) → (−3, 4), (4, 2) → (−6, 2)
  3. 3Join (−3, 2), (−6, 2), (−3, 4)

AnswerCorrect reflection, points (−3, 2), (−6, 2), (−3, 4)

Stuck on a step? Read the free lesson: Quadrilateral Properties

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Also searched as: 0580/32/M/J/23 · 0580_s23_qp_32 · 0580 s23 32 · question 6.
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