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WMA11/01 Jan 2022, Question 8: Perpendicular Lines

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 9 marks

The question, in short

Work with line l₁: 2x − 5y + 7 = 0, point A(6, −2), perpendicular line l₂ through A, intersection M, and square ABCD with diagonals meeting at M.

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

Part (a) · 1 mark

Find the gradient of the line l₁ from its equation.

  1. 15y = 2x + 7
  2. 2y = (2/5)x + 7/5, so the gradient is 2/5

Answer2/5

Part (b) · 3 marks

Find the equation of l₂ through A perpendicular to l₁, in the form y = mx + c.

  1. 1Perpendicular gradient = −1 ÷ (2/5) = −5/2
  2. 2y + 2 = −(5/2)(x − 6)
  3. 3y = −(5/2)x + 15 − 2 = −(5/2)x + 13

Answery = −(5/2)x + 13

Part (c) · 3 marks

Using algebra with full working, find the coordinates of the intersection point M of l₁ and l₂.

  1. 1Set equal: −(5/2)x + 13 = (2/5)x + 7/5
  2. 2Multiply by 10: −25x + 130 = 4x + 14
  3. 329x = 116, so x = 4
  4. 4y = −(5/2)(4) + 13 = 3, so M(4, 3)

AnswerM(4, 3)

Part (d) · 2 marks

Given the diagonals of square ABCD meet at M, find the coordinates of C.

  1. 1The diagonals of a square bisect each other, so M is the midpoint of AC
  2. 2C = 2M − A = (2 × 4 − 6, 2 × 3 − (−2))
  3. 3C = (2, 8)

AnswerC(2, 8)

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