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4024/21 Oct/Nov 2024, Question 7: Perpendicular Lines

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 10 marks

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The question, in short

Parallelogram ABCD with A(−3, 7), B(2, 5) and vector AD = (−1, −6). Find D, the length of AD, vector AC, and the equation of the line through D perpendicular to AB.

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

Part (a) · 1 mark

Find the coordinates of point D.

  1. 1D = (−3 + (−1), 7 + (−6)) = (−4, 1)

Answer(−4, 1)

Part (b) · 2 marks

Find the magnitude of vector AD.

  1. 1|→AD| = √((−1)² + (−6)²) = √37
  2. 2= 6.082… ≈ 6.08

Answer6.08 or 6.082 to 6.083

Part (c) · 3 marks

Find the column vector AC.

  1. 1→AB = (2 − (−3), 5 − 7) = (5, −2)
  2. 2→BC = →AD = (−1, −6)
  3. 3→AC = →AB + →BC = (5 − 1, −2 − 6) = (4, −8)

Answercolumn vector (4, −8)

Part (d) · 4 marks

Find the equation of line L through D perpendicular to AB.

  1. 1Gradient AB = (5 − 7)/(2 − (−3)) = −2/5
  2. 2Gradient of L = 5/2
  3. 3Through D(−4, 1): 1 = 5/2 × (−4) + c, so c = 11
  4. 4y = (5/2)x + 11

Answery = (5/2)x + 11

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Also searched as: 4024/21/O/N/24 · 4024_w24_qp_21 · 4024 w24 21 · question 7.
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