Raghav starts from Point A and drives 7 km towards west. He then takes a right turn, drives 4 km, turns right and drives 11 km. He then takes a right turn and drives 10 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.)
6 km to the north
Take Point A as the origin (0, 0), with east as +x and north as +y. A right turn while facing west points north, facing north points east, facing east points south, and facing south points west.
| Step | Move | Position (x, y) |
|---|---|---|
| Start | Point A | (0, 0) |
| 1 | 7 km west | (−7, 0) |
| 2 | Right turn → 4 km north | (−7, 4) |
| 3 | Right turn → 11 km east | (4, 4) |
| 4 | Right turn → 10 km south | (4, −6) |
| 5 | Right turn → 4 km west | (0, −6) = P |
Point P is at (0, −6), which is directly south of A at a distance of 6 km.
To return to A from P, Raghav must drive 6 km towards the north.
Hence, the answer is 6 km to the north.
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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.)
