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A man walks 12 km towards the North, turns right and walks 7 km, then turns right again and walks 12 km. How far is he from his starting point?
7 km
12 km
19 km
5 km
7 km
When opposite directional movements cover the exact same distance (12 km North and 12 km South), they completely cancel each other out, leaving only the perpendicular displacement.
When opposite directional movements cover the exact same distance (12 km North and 12 km South), they completely cancel each other out, leaving only the perpendicular displacement.
Initial North Movement
The man starts from a reference point and walks 12 km North along the vertical axis.
First Right Turn (East)
He turns right (facing East) and walks 7 km horizontally.
Second Right Turn (South) & Final Position
He turns right again (facing South) and walks 12 km. Since his 12 km South movement completely offsets his 12 km North movement, his final position is 7 km directly East of his starting point.
B: 12 km represents the length of a single vertical leg, not the distance from the start. C: 19 km is the sum of the first two segments (12 + 7) without accounting for the return path. D: 5 km is an incorrect arithmetic difference.
A is correct because the 12 km North and 12 km South movements cancel out vertically, leaving a net horizontal distance of 7 km from the starting point.
Always look for opposite directional movements (North/South or East/West) that cancel out equal distances to immediately simplify direction-and-distance problems.