Akshay starts from Point A and drives 12 km towards the north. He then takes a right turn, drives 15 km, turns right and drives 17 km. He then takes a right turn and drives 18 km. He takes a final right turn, drives 5 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 east
Set up a coordinate grid with Point A at the origin (0, 0). North = +y, East = +x.
Move 1: North 12 km → position (0, 12).
Turn right (now facing East). Move 2: East 15 km → position (15, 12).
Turn right (now facing South). Move 3: South 17 km → position (15, 12 − 17) = (15, −5).
Turn right (now facing West). Move 4: West 18 km → position (15 − 18, −5) = (−3, −5).
Turn right (now facing North). Move 5: North 5 km → position (−3, −5 + 5) = (−3, 0).
Point P is at (−3, 0) and Point A is at (0, 0).
Displacement from P to A: (0 − (−3), 0 − 0) = (3, 0), i.e., 3 km due East.
Hence, Akshay must drive 3 km to the east to reach Point A from Point P.
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Important Questions from Direction and Distance Turns
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A. 35
B. 20
C. 25
D. 40
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In which direction is the man facing now?
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