Nitin starts from Point A and drives 12 km towards south. He then takes a left turn, drives 15 km, turns left and drives 14 km. He then takes a left turn and drives 19 km. He takes a final left turn, drives 2 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.)
4 km to the east
Take Point A as the origin (0, 0), with east as positive x and north as positive y. Driving 12 km south takes Nitin to (0, –12).
Facing south, a left turn means facing east: 15 km east takes him to (15, –12). Another left turn means facing north: 14 km north takes him to (15, 2).
A left turn from north means facing west: 19 km west takes him to (15 – 19, 2) = (–4, 2). A final left turn from west means facing south: 2 km south takes him to (–4, 0), which is Point P.
| Leg | Direction | Distance | Position after the leg |
| 1 | South | 12 km | (0, –12) |
| 2 | East | 15 km | (15, –12) |
| 3 | North | 14 km | (15, 2) |
| 4 | West | 19 km | (–4, 2) |
| 5 | South | 2 km | (–4, 0) = P |
Point P is 4 km west of Point A on the same east–west line, so to reach A again Nitin must drive 4 km to the east.
Check: total east–west movement is 15 km east – 19 km west = 4 km west, and total north–south movement is 12 + 2 = 14 km south against 14 km north = 0, so P lies exactly 4 km west of A.
Hence, 4 km to the east.
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Important Questions from Direction and Distance
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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
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