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Tapan starts from Point A and drives 8 km towards the south. He then takes a right turn, drives 5 km, turns right and drives 12 km. He then takes a right turn and drives 9 km. He takes a final right turn, drives 4 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90┬░ turns only unless specified.)
4 km to the west
7 km to the west
5 km to the west
6 km to the west
4 km to the west
Track net displacement on X and Y axes separately: Net X = Right - Left, Net Y = South - North. Net X = 5 - 9 = -4 (4 West), Net Y = 8 + 12 - 4 = 16 (16 South). The reverse displacement needed is 4 km East (relative to P) to reach original longitude, but the question asks for distance from P to A.
Track net displacement on X and Y axes separately: Net X = Right - Left, Net Y = South - North. Net X = 5 - 9 = -4 (4 West), Net Y = 8 + 12 - 4 = 16 (16 South). The reverse displacement needed is 4 km East (relative to P) to reach original longitude, but the question asks for distance from P to A.
Coordinate Mapping
Starting at (0,0): South 8km is (0, -8). Right turn (West) 5km is (-5, -8). Right turn (North) 12km is (-5, 4). Right turn (East) 9km is (4, 4). Right turn (South) 4km is (4, 0).
Verification of End Point
Point P is at coordinates (4, 0). Since Point A is (0, 0), Tapan is 4 units East of Point A.
Required Correction
To return to (0,0) from (4,0), he must travel 4 km to the West.
B: 7 km west is incorrect as displacement is only 4 km. C: 5 km west is incorrect as it overshoots the origin. D: 6 km west is incorrect as it does not match the final coordinate alignment.
A is correct because Tapan's path lands him 4 km East of Point A, requiring a 4 km travel to the West to return to the starting point.
Always draw a mini-coordinate system for complex multi-turn problems. It prevents confusion between absolute orientation and relative directions.
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