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0580/43 May/Jun 2025, Question 13: Perpendicular Lines

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 6 marks

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The question, in short

Line L is y = 2(x − 5). Find its y-axis crossing, its x-value where y = 19, and the equation of perpendicular line P through (2, 3) in y = mx + c form.

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Part (a) · 1 mark

Find the coordinates where line L crosses the y-axis.

  1. 1At the y-axis x = 0: y = 2(0 − 5) = −10
  2. 2Coordinates (0, −10)

Answer(0, −10)

Part (b) · 2 marks

Find the x-coordinate where line L meets y = 19.

  1. 119 = 2(x − 5)
  2. 219 = 2x − 10
  3. 32x = 29
  4. 4x = 14.5

Answer14.5 or 14 1/2

Part (c) · 3 marks

Line P is perpendicular to L and passes through (2, 3). Find its equation as y = mx + c.

  1. 1y = 2x − 10, so gradient of L = 2
  2. 2Gradient of P = −1/2
  3. 33 = −1/2 × 2 + c, so c = 4
  4. 4y = −(1/2)x + 4

Answery = −(1/2)x + 4 or y = −0.5x + 4

Stuck on a step? Read the free lesson: Perpendicular Lines

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Also searched as: 0580/43/M/J/25 · 0580_s25_qp_43 · 0580 s25 43 · question 13.
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