Starting at station P, a survey team moves 33 km West, then 24 km South, then 21 km East, then 19 km North. Find the straight-line distance between its final position and P.

Last Updated: 07 Sept 2026

A13 km

B15 km

C11 km

D97 km

Correct Answer: 13 kmYour Answer: A

Explanation

Step 1: Mark the starting point as O(0,0) and choose East as +x and North as +y. | Step 2: Horizontal calculation: −33 + +21 = -12 km; hence the final point is west of O by 12 km. | Step 3: Vertical calculation: −24 + +19 = -5 km; hence it is south of O by 5 km. | Step 4: The two remaining components are perpendicular, so form a right triangle with sides 12 km and 5 km. | Step 6: The total route is 97 km, but that is not the required shortest distance; the direct displacement is 13 km. | Final Answer: Option A — 13 km.

Important Notes

Separate total path length from displacement; the question asks for the straight-line gap between start and finish. |
Use East = +x, West = −x, North = +y and South = −y. |
Combine all horizontal moves and all vertical moves before using a formula. |
A route may be long while its displacement is small, so never add every segment unless total distance is requested. |
Recheck squares, the square root and rounding before marking the answer.

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Starting at station P, a survey team moves 33 km West, then 24 km South, then 21 km East, then 19 km North. Find the straight-line distance between its final position and P.

Explanation

Important Notes

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