Question:

Y travels 15 kilometers due South, then 5 km due West, then 18 km due North, then 3 km due South, then 5 km due East. How far is he from the starting point?

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In direction problems, track movements along x (East–West) and y (North–South) axes separately. The net displacement is the vector sum of these components.
Updated On: Aug 12, 2025
  • 6 km
  • 3 km
  • 0 km
  • 9 km
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The Correct Option is C

Solution and Explanation

Step 1: Start at the origin (0, 0). First movement is 15 km due South → new position = (0, −15).
Step 2: Move 5 km due West → new position = (−5, −15).
Step 3: Move 18 km due North → y-coordinate changes: (−5, −15 + 18) = (−5, 3).
Step 4: Move 3 km due South → y-coordinate changes: (−5, 3 − 3) = (−5, 0).
Step 5: Move 5 km due East → x-coordinate changes: (−5 + 5, 0) = (0, 0).
Step 6: Final position = (0, 0), which is exactly the starting point.
Step 7: Therefore, distance from the starting point = \( \sqrt{(0 - 0)^2 + (0 - 0)^2} = 0 \) km.
Step 8: Elimination:
- Option (a) 6 km — would be correct if there was a diagonal offset, but here we end at origin.
- Option (b) 3 km — incorrect, partial y-offset only.
- Option (d) 9 km — incorrect, no such offset here.
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