Answer to Question #137547 in Analytic Geometry for jessica

Question

A pizza chain guarantees delivery in 30 minutes or less. All orders are processed through a central office whose job, when an order is received, is to find the closest store in order to minimize the distance for its drivers. The company has set up a grid system, similar to the Cartesian plane, to locate its stores. The lines on the grid represent the major streets that run north-south and east-west.

In the portion of the company's grid map shown, the pizza chain has stores at locations A(-8,5), B(9,-3) and C(9,5 . If a pizza is to be delivered to a location in the grid at the origin, which store should the central office call?

Answer 1

Let point O=(0,0) - the origin.

We can't move directly from one point to another, so we move north-south and east-west.

This distance is measured like $\rho$ = $|x-x_0|+|y-y_0|$, where ($x,y$ ) starting point and ($x_0,y_0$ ) end point.

Then distance between A and O is:

$\rho=|-8-0|+|5-0|=13.$

Distance between B and O is:

$\rho=|9-0|+|-3-0|=12.$

Distance between C and O is:

$\rho=|9-0|+|5-0|=14.$

So the answer on question is point B.