Question

Two people meet in the purple room on the fourth floor of a building. On departure, one person travels West 20 feet, South 12 feet, and Down 12 feet. The other person travels North 20 feet, East 10 feet, and Up 12 feet. How far apart are the two people? Round to the nearest tenth.

Answer 1

50 feet

Explanation:

Set up a 3-dimensional coordinate system (see the attached image).

This setup shows an axis that runs North-South (South is negative, North is positive), an axis that runs East-West (East is positive, West is negative), and an axis that runs Up-Down (Up is positive, Down is negative).

The two points in question are then:

First person's location (12, -20, -12), and the second person's location is (-20, 10, 12).

The distance between two points
`\left( x_1,\,y_1,\,z_1\right)` and
`\left( x_2,\,y_2,\,z_2\right)` is

`d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2`

`d=√((-20-12)^2+(10-(-20))^2+(12-(-12))^2)\\\\d=√((-32)^2+30^2+24^2)\\\\d=√(2500)\\\\d=50`