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A person walks 6 meters towards South, then turns right and walks 8 meters. He turns left and walks 5 meters, then turns left again and walks 8 meters. What is the distance between his starting point and final position?
11 meters
12 meters
13 meters
14 meters
11 meters
Map the moves on a Cartesian plane: (x, y). Starting point is (0, 0). South is -y, North is +y, East is +x, West is -x.
Map the moves on a Cartesian plane: (x, y). Starting point is (0, 0). South is -y, North is +y, East is +x, West is -x.
Track Movement Coordinates
Starting at (0, 0): Move 6m South leads to (0, -6). Turn right (West) and walk 8m leads to (-8, -6). Turn left (South) and walk 5m leads to (-8, -11). Turn left (East) and walk 8m leads to (0, -11).
Calculate Displacement
The final position is (0, -11). The distance from the starting point (0, 0) to the final position (0, -11) is the absolute value of the change in y-coordinate, which is 11 meters.
B: 12 meters is mathematically incorrect as the vertical displacement is 6+5=11 and horizontal is 8-8=0. C: 13 meters is incorrect as it assumes a diagonal that does not exist here. D: 14 meters is incorrect as it does not match the sum of displacements.
A is correct because the net horizontal displacement is 0 (8m West + 8m East) and the net vertical displacement is 11m South (6m + 5m), resulting in a straight-line distance of 11 meters from the starting point.
When movements form a 'Z' or 'S' shape, always check if horizontal movements cancel out; if they do, the total distance is simply the sum of vertical movements.