Question

In going from one city to another, a car whose driver tends to get lost goes 30km North, 50km west, and 20km southeast Approximately how far apart are the cities?

Answer 1

39.21 km

Explanation:

To determine the answer we track each move just like this:

Coordinates at the start (city A): (0, 0)

Coordinates after going 30 km north: (0, 30)

Coordinates after going 50 km west: (-50, 30)

Southeast is a move down and to the right of 45°, so we calculate at each coordinate, like this:

We calculate the distance between both points as follows:

`\begin{gathered} d=√((x_2-x_1)^2+(y_2-y_1)^2) \\ \\ \text{ we replacing} \\ \\ d=√(\left(-35.86-0\right)^2+\left(15.86-0\right)^2) \\ \\ d=√(1285.9396+251.5396)=√(1537.4792) \\ \\ d=39.21\text{ km} \end{gathered}`

The distance between both cities is 39.21 km