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IB Mathematics: Applications and Interpretation HL · 12.8: Voronoi Diagrams · 12.8.6

The toxic waste dump problem Problem set A Answers

Skills

    1. (a) \(\sqrt{130}\)
    2. (b) 12.5
    1. (a) All three distances are \(\sqrt{13}\)
    2. (b) 3.61 units
    1. (a) P: 3.61; Q: 3.04; R: 3.72
    2. (b) R(4.5, 2.25)
    3. (c) 3.72 units

In context

    1. (a) (3.5, 3.5)
    2. (b) 3.54 units
    1. (a) \(y=\dfrac{1}{3}x+\dfrac{13}{3}\)
    2. (b) \(x=2\)
    3. (c) (2, 5)
    4. (d) 7.07 units
    1. (a) (4.5, 4.5); 2.92 units
    2. (b) Yes. 2.92 is at least 2.5.

Stretch

    1. (a) 2.92 units
    2. (b) (0, 0): 3.16; (9, 0): 2.24; (9, 7): 2.83; (0, 7): 6.71. Farthest corner: (0, 7)
    3. (c) At the corner (0, 7), 6.71 units from B
    1. (a) (5.5, 3.5); 3.54 units
    2. (b) 39.3 square units

jmaths.xyz · AI HL · 12.8.6 The toxic waste dump problem