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4024/21 Oct/Nov 2021, Question 8: Equation of a Line Through Two Points

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 7 marks

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The question, in short

Given points A(−2, 3) and B(4, 5), work out the midpoint of AB, verify the given equation for line AB, and determine the perpendicular bisector's equation.

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

Part (a) · 1 mark

Calculate the coordinates of the midpoint between A(−2, 3) and B(4, 5).

  1. 1Midpoint = ((−2 + 4)/2, (3 + 5)/2) = (1, 4)

Answer(1, 4)

Part (b) · 3 marks

Demonstrate that the straight line through A(−2, 3) and B(4, 5) has equation 3y = x + 11.

  1. 1Gradient = (5 − 3)/(4 − (−2)) = 2/6 = 1/3
  2. 2y = 1/3 x + c through (4, 5): 5 = 4/3 + c → c = 11/3
  3. 3y = 1/3 x + 11/3 → 3y = x + 11

AnswerRearrangement to c = 11/3 and hence showing 3y = x + 11

Part (c) · 3 marks

Determine the equation of the line that cuts AB at right angles through its midpoint.

  1. 1Perpendicular gradient = −1 ÷ 1/3 = −3
  2. 2Through (1, 4): 4 = −3 × 1 + c → c = 7
  3. 3y = −3x + 7

Answery = −3x + 7

Stuck on a step? Read the free lesson: Equation of a Line Through Two Points

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Also searched as: 4024/21/O/N/21 · 4024_w21_qp_21 · 4024 w21 21 · question 8.
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