DP Mathematics: Applications and Interpretation Questionbank

Find the equation of the perpendicular bisector of $\text{[AB]}$ . Give your equation in the form $y=mx+c$.

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.

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

Town $\text{C}$ is due north of town $\text{A}$ and the road passes through town $\text{C}$.

Find the $y$-coordinate of town $\text{C}$.

Find the equation of the line that the road follows.

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 $a$, $b$, $d\in \mathbb{Z}$.

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

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

Calculate the gradient of the line segment AE.

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

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

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.

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

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