Question

1.9.2 who is closest? an exploration of the perpendicular bisector
here is a city with three locations of dominoes pizza.

1. the company wants to break the city down into regions so that whenever someone orders from an address, their order is sent to the store closest to their home. they have hired you to decide how to partition the city between the 3 stores.

use the applet below to show where your partitions should be.

1. if there are 100 employees, how should they be distributed among the three locations? explain your reasoning.

Explanation:

Step1: Partition the city

Draw the perpendicular bisectors between each pair of the three Dominoes Pizza store locations. The regions formed by these perpendicular bisectors will be the partitions such that any point in a region is closest to the corresponding store.

Step2: Distribute employees

A reasonable approach could be to distribute employees proportionally to the area of each partition. First, measure or calculate the area of each partition formed in Step 1. Let the areas of the three partitions be $A_1$, $A_2$, and $A_3$. The total area $A = A_1+A_2 + A_3$. Then the number of employees for each store, $n_1$, $n_2$, $n_3$ can be calculated as $n_1=\frac{A_1}{A}\times100$, $n_2=\frac{A_2}{A}\times100$, $n_3=\frac{A_3}{A}\times100$. Round these values to the nearest whole - number if necessary.

Answer:

1. Partition the city using perpendicular bisectors between the store locations.
2. Distribute employees proportionally to the area of each partition formed by the perpendicular bisectors.