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Kartik starts from Point A and drives 19 km towards the south. He then takes a left turn, drives 13 km, turns left and drives 24 km. He then takes a left turn and drives 22 km. He takes a final left 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.)
8 km to the east
9 km to the east
8 km to the west
9 km to the west
9 km to the east
Track the net displacement by assigning signs: South/West as negative and North/East as positive. Final position - Initial position gives the vector to return.
Track the net displacement by assigning signs: South/West as negative and North/East as positive. Final position - Initial position gives the vector to return.
Coordinate mapping
Set Point A at (0, 0). Movement 1: 19 km South тЖТ (0, -19). Movement 2: Left turn (facing East) 13 km тЖТ (13, -19). Movement 3: Left turn (facing North) 24 km тЖТ (13, 5). Movement 4: Left turn (facing West) 22 km тЖТ (-9, 5). Movement 5: Left turn (facing South) 5 km тЖТ Point P is at (-9, 0).
Calculate return vector
Point P is at (-9, 0) relative to A (0, 0). To reach A from P, one must move +9 in the X-direction (East) and 0 in the Y-direction. Thus, the required movement is 9 km to the East.
A: 8 km to the east is incorrect as the calculated X-displacement is 9 km; C: 8 km to the west moves further away from the origin; D: 9 km to the west moves the person to -18 on the X-axis.
B is correct because the net displacement of Kartik from Point A is 9 km to the West, meaning he must travel 9 km to the East to return to the starting point.
When multiple turns are involved, always maintain a mental or rough sketch grid; treating South/West as negative coordinates simplifies the math significantly.
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