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0580/32 Feb/Mar 2023, Question 5: Area of a Triangle

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 16 marks

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The question, in short

Use the grid diagram of triangles A, B and C to measure an angle, complete word statements, find an area, describe transformations, and draw images.

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

Part (a) · 1 mark

Measure angle c marked at the vertex (2, 0) in triangle C.

  1. 1Angle c is between the vertical side (2, 0) to (2, −6) and the side (2, 0) to (−1, −9)
  2. 2tan c = 3/9, so c ≈ 18.4°
  3. 3Measured angle c = 18°

Answer18 (accept 16 to 20)

Part (bi) · 1 mark

Choose one word from the box to describe angle c.

  1. 1c is less than 90°
  2. 2Angle c is acute

AnswerAcute

Part (bii) · 1 mark

Choose a different word from the box to describe the relationship between triangles A and C.

  1. 1Triangle C is the same shape and size as triangle A (a rotation of it)
  2. 2Triangles A and C are congruent

AnswerCongruent

Part (c) · 3 marks

Calculate the area of triangle A and state its units.

  1. 1Base = side from (2, 0) to (2, 6) = 6 cm
  2. 2Height = horizontal distance to (5, 9) = 5 − 2 = 3 cm
  3. 3Area = 6 × 3 ÷ 2 = 9 cm²

Answer9 cm²

Part (di) · 3 marks

Fully describe the single transformation mapping triangle A onto triangle B.

  1. 1Side (2, 0) to (2, 6) of length 6 maps to (−2, 0) to (−2, 2) of length 2, so scale factor = 2/6 = 1/3
  2. 2Lines through corresponding vertices, e.g. (5, 9) to (−1, 3) and (2, 0) to (−2, 0), meet at (−4, 0)
  3. 3Enlargement, centre (−4, 0), scale factor 1/3

AnswerEnlargement, centre (−4, 0), scale factor 1/3

Part (dii) · 3 marks

Fully describe the single transformation mapping triangle A onto triangle C.

  1. 1(2, 0) stays fixed, (2, 6) → (2, −6), (5, 9) → (−1, −9)
  2. 2Each point turns half a turn about (2, 0)
  3. 3Rotation, centre (2, 0), 180°

AnswerRotation, centre (2, 0), 180°

Part (ei) · 2 marks

Draw triangle A's image after translation by the column vector (3, −10).

  1. 1Add 3 to each x-coordinate and subtract 10 from each y-coordinate
  2. 2(2, 0) → (5, −10), (2, 6) → (5, −4), (5, 9) → (8, −1)
  3. 3Draw the triangle with vertices (8, −1), (5, −4), (5, −10)

AnswerCorrect translation, vertices at (8, −1), (5, −4), (5, −10)

Part (eii) · 2 marks

Draw triangle A's image after reflection in the line x = 4.

  1. 1Draw the mirror line x = 4; each point moves to the same distance on the other side
  2. 2(2, 0) → (6, 0), (2, 6) → (6, 6), (5, 9) → (3, 9)
  3. 3Draw the triangle with vertices (3, 9), (6, 6), (6, 0)

AnswerCorrect reflection, vertices at (3, 9), (6, 6), (6, 0)

Stuck on a step? Read the free lesson: Area of a Triangle

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Also searched as: 0580/32/F/M/23 · 0580_m23_qp_32 · 0580 m23 32 · question 5.
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