IB Mathematics Applications & Interpretation Question Type 1: Finding the Closest Site for a Given Point in a Voronoi Diagram Exercises

Sites lie at $S_1(0,0)$, $S_2(3,0)$ and $S_3(8,0)$ inside the rectangle $0\le x\le 10$, $0\le y\le 5$. Find the area of the Voronoi cell for $S_2$ within the rectangle.

Given sites $S_1(0,1)$, $S_2(2,5)$ and $S_3(4,2)$, determine which site is nearest to $P(1,3)$.

On the square defined by $0\le x\le 4$ and $0\le y\le 4$, five sites are located at the center and the midpoints of the sides: $(2,2)$, $(4,2)$, $(2,4)$, $(0,2)$, and $(2,0)$.

Find the area of the Voronoi cell for the center site $(2,2)$.

In the square region defined by $0\le x\le 6$ and $0\le y\le 6$, two sites are located at $S_1=(2,3)$ and $S_2=(4,3)$.

Calculate the area of the Voronoi cell for $S_1$.

Given sites $S_1=(0,0)$, $S_2=(4,0)$ and $S_3=(0,4)$, find the site(s) closest to point $P=(2,1)$.

The coordinates of three sites are $A(2,3)$, $B(5,1)$, and $C(6,4)$. Determine which site is closest to the point $P(4,3)$.

Within the triangle with vertices $(0,0)$, $(6,0)$ and $(0,6)$, three sites are placed at these vertices. Find the area of the Voronoi region for the site at $(0,0)$, restricted to the triangle.

Sites are at $(0,0)$, $(5,0)$, $(0,5)$ and $(5,5)$. Identify the nearest site to point $P=(3,2)$.

Five sites are $A(1,2)$, $B(3,5)$, $C(6,1)$, $D(4,4)$ and $E(2,6)$. Which site is closest to $P(3,3)$?

In the square $0\le x,y\le 4$, five sites are located at the four corners $(0,0)$, $(4,0)$, $(4,4)$, $(0,4)$ and the center $(2,2)$. Determine the area of the Voronoi region for the center site.

Given sites $S_1=(0,0)$ and $S_2=(3,0)$, determine which site is closest to point $P=(1,2)$.

Consider the rectangle $0\le x\le 6$, $0\le y\le 4$ with two sites $S_1=(0,0)$ and $S_2=(6,0)$. Find the area of the Voronoi cell of $S_1$ within this rectangle.