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Santhosh starts from his home and drives 5 km towards the east. He then takes a right turn, drives 8 km, turns left, and drives 3 km. He then takes a right turn and drives 5 km and turns left, then drives 3 km to reach his office. In which direction is the office with respect to his home? (All turns are 90┬░ turns only, unless specified.)
North-east
South-east
North
West
South-east
Track the Cartesian coordinates starting from (0,0); horizontal movements represent X-axis and vertical movements represent Y-axis.
Track the Cartesian coordinates starting from (0,0); horizontal movements represent X-axis and vertical movements represent Y-axis.
Calculate horizontal displacement (X-axis)
Start (0,0). Move East 5 (+5X), move East 3 (+3X), move East 5 (+5X). Total East = 5+3+5 = 13 units East.
Calculate vertical displacement (Y-axis)
Move South 8 (-8Y), move South 3 (-3Y). Total South = 8+3 = 11 units South.
Determine final direction
The final position is at (13, -11) relative to origin (0,0). Since X is positive (East) and Y is negative (South), the direction from home to office is South-east.
A: North-east is incorrect because the net Y displacement is negative. C: North is incorrect because both vertical movements are in the South direction. D: West is incorrect because all horizontal movements are in the East direction.
B is correct because the cumulative displacement results in a positive horizontal movement (East) and a negative vertical movement (South), placing the destination in the South-east quadrant.
When solving complex direction problems, always break down movements into net X (East-West) and net Y (North-South) components to avoid errors.
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