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Kartik starts from Point A and drives 42 km towards South. He then takes a left turn, drives 25 km, turns left and drives 12 km. He then takes a left turn and drives 20 km. He takes a final right turn, drives 30 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 otherwise specified.)
5 km towards West
5 km towards South
5 km towards East
5 km towards North
5 km towards West
Track the net displacement by assigning coordinate offsets: North/South as Y-axis and East/West as X-axis. A to P net movement determines the reverse return vector.
Track the net displacement by assigning coordinate offsets: North/South as Y-axis and East/West as X-axis. A to P net movement determines the reverse return vector.
Mapping the path
Start A (0,0). South 42km: (0, -42). Left turn (East) 25km: (25, -42). Left turn (North) 12km: (25, -30). Left turn (West) 20km: (5, -30). Final Right turn (North) 30km: (5, 0).
Calculate net displacement
After driving 30 km North, Kartik reaches (5, 0). Since starting Point A was (0,0), Point P is at (5, 0), which is 5 km East of A.
Determine return direction
To get from P (5, 0) back to A (0, 0), one must move 5 km towards West.
B: Incorrect direction (South). C: Incorrect direction (East). D: Incorrect direction (North).
A is correct because Point P is located 5 km East of Point A, so Kartik must drive 5 km towards West to return to Point A.
Always draw a coordinate grid for complex movement problems. Displacement is the difference between final and initial coordinates, independent of the total distance traveled.
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