3.6 Voronoi diagramsIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 3.6 Voronoi diagrams

1. A Voronoi diagram is drawn for three schools, which are the sites $A(2,1)$, $B(10,1)$ and $C(6,9)$. Coordinates are in km.
   Find the equation of the edge between the cells of $A$ and $C$.2 marks
2. Rainfall is recorded at three weather stations: $P(1,2)$ recorded 120 mm, $Q(7,2)$ recorded 80 mm and $R(4,8)$ recorded 60 mm. Coordinates are in km. The rainfall at any other point is estimated by nearest neighbour interpolation, using the Voronoi diagram of the three stations.
   A town $T$ is at $(4,6)$. Find the distance from $T$ to each station, and hence estimate the rainfall at $T$.2 marks
3. A company plans to build a waste facility as far as possible from its nearest village, at a vertex of the Voronoi diagram of three villages $V_1(0,0)$, $V_2(8,0)$ and $V_3(2,6)$. Coordinates are in km. In the Voronoi diagram, the edge between the cells of $V_1$ and $V_2$ is $x=4$, and the edge between the cells of $V_2$ and $V_3$ is $y=x-2$.
   Find the equation of the edge between the cells of $V_1$ and $V_3$, giving your answer in the form $x+3y=d$.3 marks