Manoj starts from Point A and drives 14 km towards East. He then takes a right turn, drives 12 km, turns right and drives 17 km. He then takes a right turn and drives 21 km. He takes a final right 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.)
9 km to the South
Place Point A at the origin (0, 0) with East as +x and North as +y. Driving 14 km East takes Manoj to (14, 0).
A right turn while facing East makes him face South; 12 km South takes him to (14, –12). A right turn while facing South makes him face West; 17 km West takes him to (14 – 17, –12) = (–3, –12).
A right turn while facing West makes him face North; 21 km North takes him to (–3, –12 + 21) = (–3, 9). The final right turn while facing North makes him face East; 3 km East takes him to Point P = (0, 9).
Point P is at (0, 9) and Point A is at (0, 0), so P lies exactly 9 km due North of A. To return to A he must drive 9 km towards the South.
Check: net East–West movement = 14 – 17 + 3 = 0 km and net North–South movement = –12 + 21 = 9 km North, so the shortest path back is 9 km in the opposite direction, South.
Hence, 9 km to the South.
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Important Questions from Direction and Distance
- Johny starts from Point A and drives 6 km towards the North. He then takes a right turn, drives 17 km, turns right and drives 13 km. He then takes a right turn and drives 8 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 to reach Point A again? (All turns are 90 degrees turns only unless specified.)
- Town Q is to the east of Town P. Town R is to the south of Town Q. Town S is to the east of Town R. Town T is to the south of Town S. Town U is to the east of Town T. What is the position of Town U with respect to Town Q?
- Binoy starts from Point Y and drives 16 km towards the north. He then takes a right turn and drives 43 km, then turns right and drives 38 km. He then takes a right turn and drives 19 km. He takes a final right turn, drives 22 km and stops at Point Z. How far (shortest distance) and in which direction should he drive in order to reach Point Y again? (All turns are 90-degree turns only unless specified.)
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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.)
