Mr. Jigmee starts from Point A and drives 29 km towards the west. He then takes a left turn, drives 11 km, turns left and drives 46 km. He then takes a left turn, drives 36 km, turns left and drives 5 km. He then takes a left turn and drives 9 km. He takes a final right turn, drives 12 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.)
16 km to the south
Place Point A at the origin and take east as positive x and north as positive y. Track the facing direction after each 90° turn.
Drive 29 km west (facing west): position becomes \((-29,\ 0)\).
Left turn while facing west means now facing south; drive 11 km south to reach \((-29,\ -11)\).
Left turn while facing south means now facing east; drive 46 km east to reach \((17,\ -11)\).
Left turn while facing east means now facing north; drive 36 km north to reach \((17,\ 25)\).
Left turn while facing north means now facing west; drive 5 km west to reach \((12,\ 25)\).
Left turn while facing west means now facing south; drive 9 km south to reach \((12,\ 16)\).
Right turn while facing south means now facing west; drive 12 km west to reach Point P at \((0,\ 16)\).
Point A is at \((0,\ 0)\) and P is at \((0,\ 16)\), so P is due north of A by 16 km. To return, Jigmee must drive 16 km due south.
Hence, the shortest distance is 16 km to the south.
Similar Questions
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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.)
- Himank starts from Point A and drives 13 km towards West. He then takes a left turn, drives 3 km, turns left and drives 16 km. He then takes a left turn and drives 6 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° turns only unless specified.)
- 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.)
