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Suresh starts from his home and drives 5 km towards the south. He then takes a left turn, drives 6 km, turns left, and drives 9 km. He then takes a left turn and drives 3 km and turns left, then drives 7 km to reach his office. In which direction is the office with respect to his home? (All turns are 90┬░ turns only, unless specified.)
West
North-west
North-east
South-east
South-east
Track net displacement on North-South (Y) and East-West (X) axes separately: Y = -5 + 9 - 3 = +1 (North) is wrong, let's recalculate displacement carefully.
Track net displacement on North-South (Y) and East-West (X) axes separately: Y = -5 + 9 - 3 = +1 (North) is wrong, let's recalculate displacement carefully.
Coordinate Mapping
Assume home is at (0,0). Step 1: South 5km = (0,-5). Step 2: Left turn (facing South, left is East) for 6km = (6,-5). Step 3: Left turn (facing East, left is North) for 9km = (6, 4). Step 4: Left turn (facing North, left is West) for 3km = (3, 4). Step 5: Left turn (facing West, left is South) for 7km = (3, -3).
Final Position Calculation
The final coordinates are (3, -3). Since X is +3 (East) and Y is -3 (South), the office is located in the South-east direction relative to the home origin (0,0).
A: West is incorrect because the final X-coordinate is positive (+3). B: North-west is incorrect because the Y-coordinate is negative (-3). C: North-east is incorrect because the Y-coordinate is negative (-3).
D is correct because the final coordinate (3, -3) places the office to the East and South of the starting origin.
When tracking turns, always note the direction you are facing before turning; turning left from South faces East, while turning left from West faces South.
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