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IB Mathematics: Applications and Interpretation SL · 12.8: Voronoi Diagrams · 12.8.3

Sites, cells, edges and vertices Problem set B Answers

Skills

    1. (a) 3 cells and 3 edges
    2. (b) \((5, 6)\)
    3. (c) A vertex
    1. (a) \(x+y=16\)
    2. (b) Vertices \((\frac{13}{2}, \frac{19}{2})\) and \((7, 9)\)
    1. (a) Site C
    2. (b) \(PC=5.10\) and \(PA=5.83\)
    1. (a) Yes
    2. (b) No

In context

    1. (a) \(x-3y=-16\)
    2. (b) The cell has vertices \((11, 3)\), \((\frac{13}{2}, \frac{15}{2})\), \((2, 6)\), \((3, 3)\)
    3. (c) Site E is the nearest to Q
    1. (a) \((2, 8)\)
    2. (b) \((6, 5)\); each distance is \(5\)
    3. (c) A and C only meet at the vertex.
    1. (a) 12 square units
    2. (b) 300 m²
    3. (c) 12.5%

Stretch

    1. (a) \(2x+y=23\) and \(x-2y=-6\)
    2. (b) \((8, 7)\)
    3. (c) Each distance is \(3.16\)
    1. (a) Vertices \((9, 1)\), \((9, 11)\), \((4, 6)\)
    2. (b) 3 edges; D is surrounded by A, B and C, so its cell is a closed triangle

jmaths.xyz · AI SL · 12.8.3 Sites, cells, edges and vertices