Question

Writing inMATH Answer the question that was posed at the beginning of the lesson.

How are the Midpoint and Distance Formulas used in emergency medicine?

Include the following in your answer:

• a few sentences explaining how to use the Distance Formula to approximate

the distance between two cities on a map, and

• which city, Lincoln or Omaha, an emergency medical helicopter should be

dispatched from to pick up a patient in Fremont.

Short answer

• We can use the distance formula to find the distance between the cities.
• Helicopter should be dispatched from Omaha.

Step-by-step solution

Step 1. Given information

Two cities are given on the map

Step 2. Concept used

Take map as coordinate system and the grids as coordinate points. We can use the formula to find the distance between the cities.

By applying distance formula, we can find the distance of Fremont from Omaha and Lincoln as well. Helicopter should dispatch from that city which has less distance from Fremont.

Step 3. Calculation

Theory behind the map,

Most maps have a superimposed grid. Think of the grid as a coordinate system and assign approximate coordinates to the two cities. Then use the Distance Formula to find the distance between the points with those coordinates.

Suppose the bottom left of the grid is the origin.

Then the coordinates of Lincoln are about$(0.7,0.2)$ the coordinates of Omaha are about$(4.4,3.9)$.

The distance from Omaha is $10\sqrt{{(1.7-4.4)}^2+{(4.6-3.9)}^2}$ or about$28$ miles.

The distance from Omaha is $10\sqrt{{(1.7-0.7)}^2+{(4.6-0.2)}^2}$or about $45$ miles.

Distance from Omaha is less. Hence helicopter must dispatch from Omaha.