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IB Maths AI SL 3.5 Perpendicular bisectors

IB Maths AI SL 3.5 Perpendicular bisectors
IB Mathematics: applications and interpretation guide, first assessment 2021

Students practise deriving equations of perpendicular bisectors using midpoint, gradient, and point–gradient form—key for Voronoi construction and vertex location.

How this is tested

  • find a perpendicular bisector using the midpoint and negative reciprocal slope
  • solve simultaneous equations of two perpendicular bisectors to locate Voronoi vertices like X or V
  • write boundary equations directly when symmetry gives horizontal or vertical lines

Question 5

[Maximum number: 5]

The following Voronoi diagram represents a map of a town. It shows the location of four bakeries, at points M(10,10), N(4,10), P(0,-5) and Q(-10,4). The town centre is at location O with coordinates (0,0).

Figure for Question 5 — IB Maths AI SL

Olga is at the town centre and wants to go to the nearest bakery.

Question 5(c)

(a)

Write down the equation of the line containing all the points that are of equal distance from bakery M and bakery N .

[ 1 ]

Question 5(d)

(b)

Find the equation of the perpendicular bisector of [MP]. marked.

[ 4 ]