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  • Perplex
    IB Math AIHL
    /
    Voronoi Diagrams
    /

    Problem Bank

    [Maximum mark: 19]

    A ​12​​km×12km​ nature reserve uses three rain gauges:

    Gauge

    Coordinates (km)

    Daily rainfall (mm)

    ​G1​​

    ​(3,3)​

    ​10​

    ​G2​​

    ​(9,3)​

    ​15​

    ​G3​​

    ​(6,9)​

    ​12​

    1. Show that the bisector of ​G2​​ and ​G3​​ is the line ​y=21​x+2.25.

      [4]

      To earn a crown, get your answer ready before you reveal the options!

    A complete Voronoi diagram is drawn of the nature reserve:


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    1. Determine the point ​P​ where the three bisectors meet.

      [4]
    2. Hence estimate the rainfall at point ​P​ to two decimal places.

      [3]
    3. Calculate the area of each gauge’s Voronoi cell and hence estimate the mean rainfall over the whole reserve. Give your answer to one decimal place.

      [8]

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