A rescue worker follows the route 31 km North, then 18 km West, then 19 km South, then 13 km East. What is the shortest distance from the starting camp?

Last Updated: 07 Sept 2026

A15 km

B11 km

C13 km

D81 km

Correct Answer: 13 kmYour Answer: C

Explanation

Step 1: Mark the starting point as O(0,0) and choose East as +x and North as +y. | Step 2: Horizontal calculation: −18 + +13 = -5 km; hence the final point is west of O by 5 km. | Step 3: Vertical calculation: +31 + −19 = 12 km; hence it is north of O by 12 km. | Step 6: The total route is 81 km, but that is not the required shortest distance; the direct displacement is 13 km.

Important Notes

Use East = +x, West = −x, North = +y and South = −y. |
A route may be long while its displacement is small, so never add every segment unless total distance is requested. |
Estimate the answer before selecting an option: the displacement must be less than or equal to the route length. |

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A rescue worker follows the route 31 km North, then 18 km West, then 19 km South, then 13 km East. What is the shortest distance from the starting camp?

Explanation

Important Notes

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