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

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

Find the coordinates of $H$, the intersection of this perpendicular bisector 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 $x-5y+27=0$.

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

Find the equation of the perpendicular bisector of the segment joining the points $P_1(2, 6)$ and $P_3(5, 9)$. Give your answer in the form $Ax + By + C = 0$, where $A, B, C \in \mathbb{Z}$.

Find the equation of the perpendicular bisector of the segment joining the points $P_1(2, 6)$ and $P_2(6, 4)$. Give your answer in the form $ax + by + d = 0$, where $a, b, d \in \mathbb{Z}$.

Give a parametric form for the perpendicular bisector of the line segment connecting $P_1(2, 6)$ 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.

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

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