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4024/21 Oct/Nov 2023, Question 3: 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

For line L with equation 4y = x − 5, find its gradient and y-axis crossing; for points A(4, 5) and B(−2, 8), find length AB and the equation of line AB in y = mx + c form.

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Part (ai) · 1 mark

Find the gradient of line L, given 4y = x − 5.

  1. 1y = 1/4 x − 5/4
  2. 2Gradient = 1/4

Answer1/4

Part (aii) · 1 mark

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

  1. 1x = 0: 4y = −5 so y = −5/4
  2. 2(0, −5/4)

Answer(0, −5/4)

Part (bi) · 2 marks

Find the length of line AB for A(4, 5) and B(−2, 8).

  1. 1AB = √((4 − (−2))² + (5 − 8)²) = √(36 + 9) = √45
  2. 2AB = 6.708… ≈ 6.71

Answer6.71 or 6.708…

Part (bii) · 3 marks

Find the equation of line AB in the form y = mx + c.

  1. 1m = (8 − 5)/(−2 − 4) = 3/−6 = −1/2
  2. 25 = −1/2 × 4 + c so c = 7
  3. 3y = −1/2 x + 7

Answery = −1/2 x + 7

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Also searched as: 4024/21/O/N/23 · 4024_w23_qp_21 · 4024 w23 21 · question 3.
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