Lemmara logoLemmaraWorked solution

0580/42 Oct/Nov 2022, Question 8: The Perpendicular Bisector

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 9 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Given midpoint M(12, 7) and endpoint A(2, 3) of line AB, find B, verify the perpendicular bisector equation 2y + 5x = 74, find n for N(2, n) on it, and find the area of triangle AMN.

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

Part (a) · 2 marks

Find the coordinates of point B given A(2, 3) and midpoint M(12, 7).

  1. 1M is halfway, so M to B is the same move as A to M.
  2. 2A to M: x goes up 10, y goes up 4.
  3. 3B = (12 + 10, 7 + 4) = (22, 11)

Answer(22, 11)

Part (b) · 4 marks

Show that the perpendicular bisector of AB has equation 2y + 5x = 74.

  1. 1Gradient AB = (7 − 3)/(12 − 2) = 2/5
  2. 2Perpendicular gradient = −5/2
  3. 3Through M(12, 7): y − 7 = −5/2(x − 12)
  4. 42y − 14 = −5x + 60
  5. 52y + 5x = 74

Answer2y + 5x = 74

Part (c) · 1 mark

Given N(2, n) lies on the perpendicular bisector, find the value of n.

  1. 12n + 5 × 2 = 74
  2. 22n = 64, n = 32

Answer32

Part (d) · 2 marks

Find the area of triangle AMN using A(2, 3), M(12, 7) and N(2, 32).

  1. 1AN is vertical from (2, 3) to (2, 32): length 29
  2. 2Height from M to AN = 12 − 2 = 10
  3. 3Area = 1/2 × 29 × 10 = 145

Answer145

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/O/N/22 · 0580_w22_qp_42 · 0580 w22 42 · question 8.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.