Starting at station P, a survey team moves 25 km South, then 20 km East, then 13 km North, then 5 km West. Find the straight-line distance between its final position and P.

Last Updated: 07 Sept 2026

A19.21 km

B21 km

C17 km

D63 km

Correct Answer: 19.21 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: +20 + −5 = 15 km; hence the final point is east of O by 15 km. | Step 3: Vertical calculation: −25 + +13 = -12 km; hence it is south of O by 12 km. | Step 4: The two remaining components are perpendicular, so form a right triangle with sides 15 km and 12 km. | Step 6: The total route is 63 km, but that is not the required shortest distance; the direct displacement is 19.21 km. | Final Answer: Option A — 19.21 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 25 km South, then 20 km East, then 13 km North, then 5 km West. Find the straight-line distance between its final position and P.

Explanation

Important Notes

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