A person walks 10 km north, then 25 km west, and finally 10 km south. How far is he from his starting point?
25 km
We track the person's movement on a north-south and east-west grid, starting from the origin.
First he walks 10 km north, reaching a point 10 km above the start.
Then he walks 25 km west, moving 25 km to the left while staying 10 km north.
Finally he walks 10 km south, which cancels the earlier 10 km north exactly.
So the north and south movements cancel, leaving a net displacement of only 25 km to the west.
The straight-line distance from the start is therefore just this westward gap = 25 km.
No diagonal (Pythagorean) step is needed because there is no leftover vertical distance.
Hence he is 25 km from his starting point.
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