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Three automobile service centers are located at A(2,8), B(8,2), C(10,10), with coordinates measured in kilometers. Emmy is drawing a Voronoi diagram with sites representing each of the centers. She has drawn two edges, as seen below.
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Describe what Emmy must draw to complete the Voronoi diagram.
Show that the missing edge has equation 4x+y−33=0.
A major car crash occurs at P =(7,7) and all vehicles involved are transported to the nearest service center.
Determine which site is closest to the crash. Justify your answer.
In the wake of the accident, it is decided that a fourth service center will be constructed. The government wants it to be located as far as possible from the three existing sites.
Determine the coordinates of the new site, D.
After D is constructed. the site needs to be stocked with tires. A truck will transport tires from each of the preexisting sites to the new site.
Starting at A, the truck drives from A→D→B→D→C.
Determine the total distance the truck will travel.
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Four villages are located at A(2,2), B(8,2), C(8,6), D(2,9). The perpendicular bisectors of every pair of villages have been drawn on a map. A toxic waste dump is to be constructed between the villages. Two candidate dump sites are the vertices P(5, 4) and Q(4, 5.5).
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Write down the equation of the perpendicular bisector [BC].
For each site P and Q:
Calculate the distance between the site and the closest village.
Hence decide which site is safer for the toxic-waste dump and justify your decision.
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