Lemmara logoLemmaraWorked solution

0606/22 Feb/Mar 2026, Question 2: The Perpendicular Bisector

Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 6 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Given A(1, 3) and B(−7, 1), with P(2, a) on the perpendicular bisector of AB, determine a, then reflect P across line AB to get Q's coordinates.

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

Part (a) · 4 marks

Work out the value of a for point P(2, a) lying on the perpendicular bisector of the segment joining A(1, 3) and B(−7, 1).

  1. 1Midpoint of AB = ((1 − 7)/2, (3 + 1)/2) = (−3, 2)
  2. 2Gradient of AB = (1 − 3)/(−7 − 1) = 1/4, so gradient of perpendicular bisector = −4
  3. 3Perpendicular bisector: y − 2 = −4(x + 3)
  4. 4At x = 2: a = 2 − 4(5) = −18

Answera = −18

Part (b) · 2 marks

Using P and the line through A and B, find the coordinates of Q, the mirror image of P in AB.

  1. 1P lies on the perpendicular bisector, which meets AB at its midpoint (−3, 2) at right angles
  2. 2So (−3, 2) is the midpoint of PQ
  3. 3Q = (2(−3) − 2, 2(2) − (−18)) = (−8, 22)

Answer(−8, 22)

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/F/M/26 · 0606_m26_qp_22 · 0606 m26 22 · question 2.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.