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IB Maths AI SL 3.6 Voronoi Diagrams Questions

Practise identifying and constructing Voronoi cells and boundaries, then using nearest-site geometry to solve planning or applied region problems with justified units.

Syllabus
First assessment 2021
Course
Mathematics: applications and interpretation SL
Level
SL

Exam points

  • Identify sites, vertices, edges, cells and nearest neighbours in a Voronoi diagram.
  • Construct or interpret boundaries and closest-site regions, including a newly added site or weighted distance condition.
  • Use Voronoi structure to determine nearest locations, boundaries or region areas in planning, disease, ecology or meteorology contexts.
  • Justify the selected cell or boundary and communicate the geometric result with appropriate units.

Learn this topic

Study SL 3.6—Voronoi diagrams conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

IB Maths AI SL 3.6 Voronoi Diagrams Questions question 1

[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 IB Maths AI SL 3.6 Voronoi Diagrams Questions question 1 — IB Maths AI SL

Question (a)

(a)

The equation of ( XY ) is y=2-x and the equation of (YZ) is y=0.5 x+3.5.

Find the coordinates of X .

[ 3 ]

Question (b)

(b)

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

Determine the exact length of [YZ].

[ 2 ]

Question (c)

(c)

Hence find the area of triangle XYZ.

[ 2 ]

Question (d)

(d)

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

State one criticism of this interpretation.

[ 1 ]
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