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0580/21 May/Jun 2021, Question 16: Perpendicular Lines

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 7 marks

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The question, in short

Using the given straight-line graph on a grid, work out its slope, its equation, and the equation of a perpendicular line through (12, −7).

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

Part (a) · 2 marks

Work out the slope of line l shown on the grid.

  1. 1Line l passes through (0, 2) and (4, −1)
  2. 2Gradient = (−1 − 2)/(4 − 0)
  3. 3= −3/4

Answer−3/4 or −0.75

Part (b) · 2 marks

Write the equation of line l as y = mx + c.

  1. 1Gradient = −3/4 and the line crosses the y-axis at (0, 2), so c = 2
  2. 2y = −3/4 x + 2

Answer−3/4 x + 2

Part (c) · 3 marks

Line l has slope −3/4. Find the equation, as y = mx + c, of the line perpendicular to l through (12, −7).

  1. 1Perpendicular gradient = −1 ÷ (−3/4) = 4/3
  2. 2−7 = 4/3 × 12 + c
  3. 3−7 = 16 + c, so c = −23
  4. 4y = 4/3 x − 23

Answery = 4/3 x − 23

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

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Also searched as: 0580/21/M/J/21 · 0580_s21_qp_21 · 0580 s21 21 · question 16.
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