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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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A 10m × 10m warehouse floor is represented by the square 0≤x≤10, 0≤y≤10.
Three robot-charging docks are located at A(2,2), B(8,2), and C(5,8). The complete Voronoi diagram is shown to workers on a screen:
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Determine the equation of the perpendicular bisector that forms the boundary between the regions of docks B and C.
A robot is currently at the point P(7,6) and begins to run low on battery.
State which dock it should drive to and provide a brief explanation why.
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Alice forgot to pack water when she hiked in the Grand Canyon this June. Due to the heat, she was unable to climb back up due to heat exhaustion. A helicopter picks her up and brings her to one of three hospitals at locations A, B, and C:
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Determine the hospital that Alice should be taken to so as to minimize transit time.
In order to save money on helicopter rides, Arizona builds a hospital on the Bright Angel Trail of the Grand Canyon. The state of Arizona wishes to update their map to reflect the construction of the new hospital (marked as V).
Draw the new boundaries of the new Voronoi diagram.
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A has coordinates (0,0), B has coordinates (−4,12), and C has coordinates (15,12).
Find the coordinates of V.
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Uraniumland has many nuclear power plants. In 1979, visitors of Uraniumland to a mountain wildlife preserve noticed that many animals seemed to be suffering from symptoms of radiation poisoning. As a result, the government conducted an observational study. At each site specified in the table below, they took a sample of 100 deer and recorded the number with symptoms.
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Based on the graph and the table provided, determine the nuclear facility with the leak.
Uraniumland wants to build a city in which energy is supplied by these three nuclear plants.
Determine a location that Uraniumland could build the city so that it is less than 4.5 units from all plants. Give the coordinates.