Question

Here's another problem about dividing up a square city based on closeness.

1. Bus lines run along two streets. The L Bus runs along L Street and the M Bus runs along M Street. People prefer to ride whicheverbus is closer to them. Divide the city into two colored regions: places closer to L street and places closer to the M street.
2. Continuing from the previous problem, the city adds a third bus line, the N bus along N street. People living closest to N street will prefer this new bus. Divide the city into three colored regions: closest to L Street, to M Street, and to N Street.
3. Continuing from the previous problem, the L bus on L street has been eliminated, but there is a new P Bus on P Street.

Divide the city into three colored regions: closest to M street, to N street, and to P street.

Answer 1

The problem deals with dividing a city grid into regions based on the closest bus lines. This requires creating equidistant lines between bus-running streets, resulting in sectors each closest to a respective bus street. Changes in bus lines lead to adjustments in the divisions.

Step-by-step explanation:

The problem at hand is about dividing a square city into regions based on the proximity to bus lines. This task involves a geometric analysis of the city layout and the bus streets.

Bus Lines Division

For the first scenario: Imagine the city as a grid, with L and M streets running parallel. The region closer to L Street and the region closer to M Street would be separated by a line equidistant from both L and M Streets. This line would effectively be a street itself, with one half of the city colored for those closer to the L Bus, and the other half for the M Bus.

In the second scenario, with the addition of the N Bus: The city is now divided into three regions. One must draw two new lines that are equidistant from L to M and M to N Streets, creating three sectors each closest to one of the streets.

For the third scenario: After the removal of the L Bus and introduction of the P Bus, the same process is applied, but now between M, N, and the new P Streets. Three regions are created, each closest to one of the remaining streets.