IB Maths AI SL 3.6 Voronoi diagrams Question Bank

Practise IB Mathematics SL/HL 3.6 by applying voronoi diagrams methods to exam-style questions.

[Maximum number: 8]

The Voronoi diagram below shows four supermarkets represented by points with coordinates A(0,0), B(6,0), C(0,6) and D(2,2). The vertices X, Y, Z are also shown. All distances are measured in kilometres.

Figure for Question SL 3.6—Voronoi diagrams question 1 — IB Maths AI SL

(a)

Find the coordinates of X .

The coordinates of Y are (-1,3) and the coordinates of Z are (7, 7).

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(b)

Determine the exact length of [YZ].

[ 2 ]

attempt to use distance formula

\begin{aligned} & \mathrm{YZ}=\sqrt{(7-(-1))^{2}+(7-3)^{2}} \\ & =\sqrt{80}(4 \sqrt{5}) \end{aligned}

(c)

Hence find the area of triangle XYZ.

A town planner believes that the larger the area of the Voronoi cell XYZ, the more people will shop at supermarket D.

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$\quad($ area $=) \frac{1}{2} \sqrt{80} \sqrt{32} \sin 71.5650 \ldots \quad$ OR $\quad($ area $=) \frac{1}{2} \sqrt{32} \sqrt{72}$ $=24 \mathrm{~km}^{2}$

(d)

State one criticism of this interpretation.

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SL 3.6—Voronoi diagrams question 1

Question (a)

Question (b)

Question (c)

Question (d)