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A person walks 12 meters towards the North, then turns left and walks 7 meters. He then turns right and walks 5 meters, and finally turns right and walks 7 meters. How far is he from the starting point?
17 meters
19 meters
24 meters
21 meters
17 meters
Track net movement by resolving North-South and East-West displacements separately, then use the Pythagorean theorem for the result.
Track net movement by resolving North-South and East-West displacements separately, then use the Pythagorean theorem for the result.
Calculate Net North-South displacement
Start at (0,0). Move North 12m: (0, 12). Move left (West) 7m: (-7, 12). Move right (North) 5m: (-7, 17). Move right (East) 7m: (0, 17).
Calculate final distance
The person ends at coordinate (0, 17) relative to the start (0, 0). The vertical distance is 17 meters and the horizontal distance is 0 meters. The total distance from the starting point is 17 meters.
B: 19 meters is incorrect as it does not follow the geometric path sum; C: 24 meters is incorrect as it assumes a simple addition of path segments ignoring direction; D: 21 meters is incorrect as it miscalculates the vertical displacement.
A is correct because the person ends up exactly 17 meters north of the starting point after moving 12m north and 5m north sequentially.
Always map direction movements on a coordinate plane (X,Y) to avoid getting confused by complex turns; horizontal (East/West) and vertical (North/South) movements cancel or add up independently.
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