Starting at station P, a survey team moves 30 km West, then 18 km South, then 21 km East, then 6 km North. Find the straight-line distance between its final position and P.

Last Updated: 07 Sept 2026

A17 km

B13 km

C75 km

D15 km

Correct Answer: 15 kmYour Answer: D

Explanation

Step 1: Mark the starting point as O(0,0) and choose East as +x and North as +y. | Step 2: Horizontal calculation: −30 + +21 = -9 km; hence the final point is west of O by 9 km. | Step 3: Vertical calculation: −18 + +6 = -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 9 km and 12 km. | Step 6: The total route is 75 km, but that is not the required shortest distance; the direct displacement is 15 km. | Final Answer: Option D — 15 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 30 km West, then 18 km South, then 21 km East, then 6 km North. Find the straight-line distance between its final position and P.

Explanation

Important Notes

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