Lemmara logoLemmaraWorked solution

0580/42 May/Jun 2022, Question 3: The Perpendicular Bisector

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 12 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

For the segment joining F(3, 2) and G(−5, 4), work out its length, the equation of its perpendicular bisector, and y-axis points H with GH = 13.

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

Part (a) · 3 marks

Work out the distance between F(3, 2) and G(−5, 4).

  1. 1Horizontal change = 3 − (−5) = 8, vertical change = 4 − 2 = 2
  2. 2Length = √(8² + 2²) = √68
  3. 3= 8.246… ≈ 8.25

Answer8.25 or 8.246…

Part (b) · 5 marks

Determine the perpendicular bisector equation for FG, giving it as y = mx + c.

  1. 1Midpoint = ((3 − 5)/2, (2 + 4)/2) = (−1, 3)
  2. 2Gradient of l = (4 − 2)/(−5 − 3) = −1/4
  3. 3Perpendicular gradient = 4
  4. 43 = 4 × (−1) + c, so c = 7
  5. 5y = 4x + 7

Answery = 4x + 7

Part (c) · 4 marks

With H on the y-axis and GH = 13, determine both coordinate pairs for H.

  1. 1H = (0, y): (−5 − 0)² + (4 − y)² = 13²
  2. 2(4 − y)² = 169 − 25 = 144
  3. 34 − y = ±12, so y = −8 or y = 16
  4. 4(0, −8) and (0, 16)

Answer(0, −8) and (0, 16)

Stuck on a step? Read the free lesson: The Perpendicular Bisector

Practise more the perpendicular bisector questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on the perpendicular bisector

Also searched as: 0580/42/M/J/22 · 0580_s22_qp_42 · 0580 s22 42 · question 3.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.