Lemmara logoLemmaraWorked solution

0606/22 Oct/Nov 2025, Question 1: The Perpendicular Bisector

Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 9 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Line y = 4x − 3 intersects curve y = 3 + 5x − 2x² at A and B; find A and B, then the area of triangle POQ formed by the perpendicular bisector of AB with the axes.

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

Part (a) · 4 marks

Solve the line and curve equations simultaneously to find the coordinates of the two intersection points A and B.

  1. 14x − 3 = 3 + 5x − 2x²
  2. 22x² − x − 6 = 0
  3. 3(2x + 3)(x − 2) = 0, x = −1.5 or x = 2
  4. 4y = 4(−1.5) − 3 = −9 and y = 4(2) − 3 = 5
  5. 5A and B are (−1.5, −9) and (2, 5)

Answer(−1.5, −9) and (2, 5)

Part (b) · 5 marks

Find the perpendicular bisector of AB, its intercepts P and Q with the axes, and the area of triangle POQ with origin O.

  1. 1Midpoint of AB = (0.25, −2)
  2. 2Gradient of AB = (5 − (−9))/(2 − (−1.5)) = 4, so perpendicular gradient = −1/4
  3. 3Perpendicular bisector: y + 2 = −(1/4)(x − 1/4), i.e. y = −(1/4)x − 31/16
  4. 4Crosses the axes at (−31/4, 0) and (0, −31/16)
  5. 5Area = ½ × 31/4 × 31/16 = 961/128 ≈ 7.51

Answer961/128 or 7.51

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

Practise more the perpendicular bisector questions

Real 0606 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: 0606/22/O/N/25 · 0606_w25_qp_22 · 0606 w25 22 · question 1.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.