Question Type 3: Constructing Voronoi Diagrams for a given number of points Exercises

Determine which of the points $P_1(2,6)$, $P_2(6,4)$ or $P_3(5,9)$ is closest to $Q(4,7)$.

Write the equation of the boundary between the Voronoi cells of $P_1(2,6)$ and $P_3(5,9)$.

Find the equation of the perpendicular bisector of the segment joining the points $P_2(6,4)$ and $P_3(5,9)$.

Find the equation of the perpendicular bisector of the segment joining the points $P_1(2,6)$ and $P_3(5,9)$.

Find the equation of the perpendicular bisector of the segment joining the points $P_1(2,6)$ and $P_2(6,4)$.

In the plane with sites $P_1,P_2,P_3$, state which Voronoi cells are unbounded and explain why.

Write the system of linear inequalities that defines the Voronoi cell of $P_2(6,4)$ relative to $P_1(2,6)$ and $P_3(5,9)$.

Find the intersection $H$ of the perpendicular bisector of $P_1P_2$ with the $x$–axis.

Find the $x$- and $y$-intercepts of the perpendicular bisector of $P_2(6,4)$ and $P_3(5,9)$ whose equation is $x-5y+27=0$.

Give a parametric form for the perpendicular bisector of the segment $P_1(2,6)$ to $P_2(6,4)$.

Find the coordinates of the intersection point of the perpendicular bisectors of $P_1P_2$ and $P_1P_3$.

Calculate the acute angle between the perpendicular bisectors of $P_1P_2$ (slope $2$) and $P_2P_3$ (slope $1/5$).