IB Maths AI HL AI 3.2 Voronoi diagrams questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

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Question 1

Paper 2Medium8 marks

A mapping team marks two transmitters, $A$ and $B$ and a straight service path $CD$ on a coordinate map. The coordinates are measured in kilometres. A receiver must be placed on $CD$ so that it is the same distance from both transmitters.

Figure 1 shows the positions of $A$ $B$ $C$ and $D$

(a)

Find the coordinates of the midpoint $M$ of $AB$

[1]

(b)

Find the equation of the perpendicular bisector of $AB$ Give your answer in the form $y=mx+c$

[4]

(c)

Hence, determine the coordinates of the receiver.

[3]

Question 2

Paper 1Hard6 marks

A flat map uses Cartesian coordinates to locate radio beacons. The segment $AB$ lies on the line $3x-4y-10=0$ and its midpoint is $M(2,-1)$

(a)

Determine the equation of the perpendicular bisector of $AB$ giving your answer in the form $ax+by+c=0$

[2]

(b)

Beacons $C$ and $D$ have coordinates $C(-2,4)$ and $D(4,2)$ An emergency receiver $Q$ must be equidistant from $A$ and $B$ and also equidistant from $C$ and $D$

Using your answer to (a), determine the exact coordinates of $Q$

[4]

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