Question

On a map, a hospital is located at (-42,7). A wreck occurs at (13,-14). How far must the Air Care helicopter fly to reach the wreck from the hospital. (Each unit on the map equals one mile.)

Answer 1

The helicopter must cover a straight line distance of approximately 61.270 miles from the hospital to the wreck site.

Explanation:

Let suppose that Air Care helicopter travels in straight line from the hospital to the wreck site, we can determine that distance (
`d`), measured in miles, by using the following Pythagorean identity from Analytical Geometry:

`d = \sqrt{(x_(W)-x_(H))^(2)+(y_(W)-y_(H))^(2)}`

Where:

`x_(W)`,
`y_(W)` - Location of the wreck site, measured in miles.

`x_(H)`,
`y_(H)` - Location of the hospital, measured in miles.

If the location of the wreck site and the hospital are
`(13, -14)` and
`(-42, 7)`, respectively. The distance that helicopter must cover is:

`d = \sqrt{[13-(-42)]^(2)+[(-14)-13]^(2)}`

`d \approx 61.270\,mi`

The helicopter must cover a straight line distance of approximately 61.270 miles from the hospital to the wreck site.