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Ajay starts from his home and drives 5 km towards the south. He then takes a left turn, drives 6 km, turns right, and drives 4 km. He then takes a left turn and drives 5 km and reached his office. In which direction is the office with respect to his home? (All turns are 90┬░ turns only, unless specified.)
South-east
North-west
South-west
North-east
South-east
Track the net displacement using a Cartesian coordinate system where the Starting point is (0,0). Move south as -Y, north as +Y, east as +X, and west as -X.
Track the net displacement using a Cartesian coordinate system where the Starting point is (0,0). Move south as -Y, north as +Y, east as +X, and west as -X.
Establish starting position
Assume home is at coordinate (0, 0).
Track movements step-by-step
1. 5 km South: (0, -5). 2. Left turn from South is East: (0+6, -5) = (6, -5). 3. Right turn from East is South: (6, -5-4) = (6, -9). 4. Left turn from South is East: (6+5, -9) = (11, -9).
Determine final direction
The final coordinate is (11, -9). Since both X and Y are positive/negative relative to origin, the movement is in the positive X (East) and negative Y (South) direction, placing the office to the South-east of the home.
B: North-west is incorrect because the net displacement is positive on X and negative on Y. C: South-west is incorrect because the horizontal displacement is East, not West. D: North-east is incorrect because the net vertical displacement is South, not North.
A is correct because the final coordinate (11, -9) relative to the origin (0, 0) clearly indicates a position in the South-east quadrant.
For complex direction problems, always visualize the path on a 2D Cartesian plane to avoid confusion from multiple turns.
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