Rohit starts from Point A and drives 10 km towards north. He then takes a left turn, drives 12 km, turns left and drives 11 km. He then takes a left turn and drives 15 km. He takes a final left turn, drives 1 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 Point A as the origin (0, 0), with north as +y and east as +x.
10 km north → (0, 10). A left turn from north faces west: 12 km west → (−12, 10).
A left turn from west faces south: 11 km south → (−12, −1).
A left turn from south faces east: 15 km east → (3, −1).
A final left turn from east faces north: 1 km north → (3, 0). This is Point P.
P is 3 km east of A on the same horizontal line, so Rohit must drive 3 km towards the west to return to A.
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.)
