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  • Perplex
    IB Math AISL
    /
    Voronoi Diagrams
    /

    Problems

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    Problem Bank - Voronoi Diagrams

    Access custom-built, exam-style problems for voronoi diagrams. Each problem has a full solution and mark-scheme, as well as AI grading and support.

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    IB: 6
    4

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    0 / 5

    Three existing water towers are located at the points

    A(0,0),B(8,0),C(0,6)

    where each grid unit represents 1km. A new water tower is to be added to the diagram. To minimize risk of flooding, the water tower is placed at point P. A Voronoi diagram of the water towers is sketched below:

    Powered by Desmos

    1. Determine:

      1. the coordinates of the point P that is equidistant from all 3 towers, and

        [3]
      2. the common distance r from P to each tower.

        [2]
    5

    !

    0 / 9

    A square park is modeled by the region 0≤x≤8 and 0≤y≤8 (all distances in meters).

    There are three refreshment kiosks.

    • Kiosk A is at the point (2,6).

    • Kiosk B is at the point (2,b).

    • Kiosk C is at the point (6,6).

    A Voronoi diagram of the park's kiosks is shown below:

    Powered by Desmos


    Every visitor is served by the nearest kiosk.

    1. Show that V has coordinates (4,5).

      [4]
    2. Determine the value of b.

      [3]
    3. Determine the fraction of the park served by Kiosk A.

      [2]
    6

    !

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