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

Sites, cells, edges and vertices Problem set A Answers

Skills

    1. (a) 3 cells and 3 edges
    2. (b) \((8, 7)\)
    3. (c) A vertex
    1. (a) \(x=6\)
    2. (b) Vertices \((6, 4)\) and \((6, 9)\)
    1. (a) Site B
    2. (b) \(PB=2.24\) and \(PA=3.16\)
    1. (a) Yes
    2. (b) No

In context

    1. (a) \(3x-y=21\)
    2. (b) The cell has vertices \((9, 6)\), \((\frac{13}{2}, \frac{17}{2})\), \((5, 4)\), \((8, 3)\)
    3. (c) Site E is the nearest to Q
    1. (a) \((3, 6)\)
    2. (b) \((7, \frac{7}{2})\); each distance is \(4.72\)
    3. (c) A and C only meet at the vertex.
    1. (a) 16 square units
    2. (b) 64 km²
    3. (c) 16.7%

Stretch

    1. (a) \(y=5\) and \(5x+3y=40\)
    2. (b) \((5, 5)\)
    3. (c) Each distance is \(4.12\)
    1. (a) Vertices \((\frac{23}{2}, \frac{3}{2})\), \((\frac{11}{2}, \frac{23}{2})\), \((\frac{7}{2}, \frac{7}{2})\)
    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