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A man walks 9 km towards the North, then turns right and walks 12 km. He then turns right again and walks 9 km. How far is he from his starting point?
12 km
9 km
21 km
15 km
12 km
Recognize that walking 9 km North and later 9 km South cancels out the vertical displacement entirely, leaving only the 12 km horizontal distance.
Recognize that walking 9 km North and later 9 km South cancels out the vertical displacement entirely, leaving only the 12 km horizontal distance.
Step 1: Initial Movements
Starting from the origin, walking 9 km North places him at a vertical coordinate of +9. Turning right (facing East) and walking 12 km moves him 12 km to the right.
Step 2: Final Movement
Turning right again means he is now facing South. Walking 9 km South brings his vertical coordinate back down by 9 km, placing him directly on the horizontal axis.
Step 3: Calculate Net Distance
Since the vertical movements (+9 and -9) completely cancel out, the final position is 12 km horizontally away from the starting point.
B: 9 km is only the length of one vertical segment. C: 21 km incorrectly sums the first two segments (9 + 12) without accounting for the return path. D: 15 km is a distractor based on the 9-12-15 Pythagorean triplet, which does not apply since the vertical offsets cancel out.
A is correct because the vertical displacements of 9 km North and 9 km South cancel each other out, leaving a net displacement of exactly 12 km along the horizontal axis from the start.
Always look for opposite directional movements (North-South or East-West) that can cancel each other out to simplify distance calculations quickly.
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