IB Mathematics Applications & Interpretation Topic SL…

The Voronoi diagram shows three sites $A(0,\,0)$ , $B(6,\,2)$ , and $C(2,\,6)$ . The boundaries between the cells are the perpendicular bisectors of the segments , , and .

(a) Find the equation of the perpendicular bisector of $[AB]$ , giving your answer in the form $y=mx+c$ .

(b) Find the equation of the perpendicular bisector of $[AC]$ , giving your answer in the form $y=mx+c$ .

(d) Verify that the Voronoi vertex is equidistant from all three sites by computing one such distance.

The Voronoi diagram shows the locations of $5$ sites: $A(0,\,4)$ , $B(8,\,4)$ , $C(4,\,0)$ , $D(4,\,8)$ , and $E(4,\,4)$ .

(a) Write down the coordinates of the four vertices of the cell of site $E$ .

(b) Hence find the area of the cell of site $E$ .

The diagram below shows a Voronoi diagram formed by five points: $A(0, 2)$ , $B(6, 2)$ , $C(6, 6)$ , $D(0, 6)$ , and $E(3, 4)$ . Each region corresponds to the area closest to one of the points.

(a) Which region corresponds to point $C$ ?

(b) Find the equation of the perpendicular bisector used to separate the regions of $A$ and $B$ .

Two sites $A$ and $B$ are placed at $A(2,\,3)$ and $B(8,\,7)$ . A point $P(9,\,2)$ is marked on the diagram.

(a) Find the equation of the perpendicular bisector of $[AB]$ , giving your answer in the form $ax+by+d=0$ , where $a$ , $b$ , $d\in\mathbb{Z}$ .

The Voronoi diagram shows the locations of $4$ weather stations $A(2,\,6)$ , $B(8,\,7)$ , $C(9,\,2)$ , and $D(3,\,1)$ , on a coordinate map with units in km. The daily rainfall, in mm, recorded at each station is shown in the table.

(b) Hence which of the sites, $A$ or $B$ , lies closer to the point $P$ . your answer.

(a) Using the diagram, the station closest to the point $P(5,\,5)$ .

(b) Use nearest-neighbour interpolation to the rainfall at $P$ .

IB Mathematics Applications & Interpretation SL 3.6—voronoi Diagrams Questionbank

IB Mathematics Applications & Interpretation SL 3.6—voronoi Diagrams Questionbank

IB Mathematics Applications & Interpretation SL 3.6—voronoi Diagrams Questionbank

IB Mathematics Applications & Interpretation SL 3.6—voronoi Diagrams Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 3.6—voronoi Diagrams Questionbank