Gor starts from Point A and drives 10 km towards north. He then takes a left turn and drives 12 km, and again turns left and drives 13 km. He then takes a left turn and drives 15 km. He takes a final left turn, drives 3 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-degree turns only unless specified.)
3 km to the west
Take A as the origin (0, 0), with north as +y and east as +x.
10 km north: (0, 10). Left from north means facing west; 12 km: (−12, 10).
Left from west means facing south; 13 km: (−12, −3). Left from south means facing east; 15 km: (3, −3).
Left from east means facing north; 3 km: P = (3, 0).
P lies on the same east–west line as A, 3 km to its east. So to return, Gor must drive 3 km towards the west.
Hence, the answer is 3 km to the west.
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Important Questions from Direction and Distance
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- Shyam starts from Point A and drives 12 km towards east. He then takes a right turn,
drives 7 km, turns right and drives 5 km. He then takes a left turn and drives 9 km. He
takes a final right turn, drives 7 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
$90^{\circ}$ turns only unless specified.)
