Find the equation of the perpendicular bisector of $\left[\text{IF}\right]$.

Sketch a Voronoi diagram showing the regions within the metropolitan area that are closest to each town.

Sketch this new Voronoi diagram showing the regions within the metropolitan area which are closest to each town.

Sketch a Voronoi diagram to represent this information.

Make one possible criticism of the council’s choice of location.

Given that the coordinates of one vertex of the new Voronoi diagram are $(20, 37.5)$, find the coordinates of the other two vertices within the metropolitan area.

Find the location of the toxic waste dump, given that this location is not on the edge of the metropolitan area.

Write down the equation of the perpendicular bisector of $\text{[PC]}$.

A new office is to be built within the triangle formed by $\text{A}$, $\text{B}$ and $\text{C}$, at a point as far as possible from the other three offices.

Find the distance of this office from each of the other offices.

Find the midpoint of $\text{[BD]}$.

The model assumes that each town is positioned at a single point. Describe possible circumstances in which this modelling assumption is reasonable.

Sketch a new Voronoi diagram to represent this new situation.

State what the shape of the land, owned by the youngest child, is.

In the context of the question, explain the significance of the Voronoi cell containing site E.

Calculate the gradient of the line segment AE.

Find how much land an older child has lost.

The diagram below is part of a Voronoi diagram.

Diagram not to scale

A and B are sites with B having the co-ordinates of (4, 6). L is an edge; the equation of this perpendicular bisector of the line segment from A to B is $y=-2x+9$

Find the co-ordinates of the point A.

State, with a reason, if all five children now own an equal amount of land.

State a further assumption that must be made in order to use area covered as a measure of whether or not the manager of office $\text{C}$ is responsible for more students than the managers of offices $\text{A}$ and $\text{B}$.

Write down the coordinates of tower $\text{T4}$.

Tower $\text{T1}$ has coordinates $(-13, 3)$.

Find the gradient of the edge of the Voronoi diagram between towers $\text{T1}$ and $\text{T2}$.

Find the equation of the line which would complete the Voronoi cell containing site E.

Give your answer in the form $ax+by+d=0$ where $a$, $b$, $d\in \mathbb{Z}$.

Find the area of the youngest child’s land.

Find the area of campus managed by office $\text{C}$.

Hence or otherwise find the areas managed by offices $\text{A}$ and $\text{B}$.

Show that the new station should be built at $\text{P}$.

Hence draw the missing boundaries of the region around $\text{P}$ on the following diagram.