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Manoj starts from his home and drives 4 km towards the north. He then takes a left turn, drives 5 km, turns right, and drives 9 km. He then takes a left turn and drives 3 km and turns left then drives 5 km to reach 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
West
North-east
North-west
Track the net North-South and East-West displacement on a coordinate system (Home = 0,0).
Track the net North-South and East-West displacement on a coordinate system (Home = 0,0).
Coordinate Mapping
Starting at (0,0): 1. Move 4 km North: (0, 4). 2. Left turn (West) 5 km: (-5, 4). 3. Right turn (North) 9 km: (-5, 13). 4. Left turn (West) 3 km: (-8, 13). 5. Left turn (South) 5 km: (-8, 8).
Final Result Analysis
The final position of the office is (-8, 8). Since the X-coordinate is negative (West) and the Y-coordinate is positive (North), the position relative to home (0,0) is North-west.
A: South-east is incorrect because the final Y-coordinate is positive (North), not negative. C: West is incorrect because there is a net displacement of 8 km North. D: North-east is incorrect because the final X-coordinate is negative (West), not positive.
B is correct because the final coordinate (-8, 8) lies in the second quadrant, which represents the North-west direction from the origin (0, 0).
In direction problems, always treat Home as the origin (0,0) and assign North/East as positive values and South/West as negative values to avoid visual errors.
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