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Dilip starts from point A and drives 6 km towards the North. He then takes a right turn and drives 2 km. He then takes a left turn and drives 3 km. He then takes a left turn and drives 7 km. He takes a final left turn and drives 9 km to reach point B. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90 degrees turns only unless specified)
6 km West
3 km East
5 km East
5 km West
5 km East
Track net displacement on North-South and East-West axes separately to determine the relative final position.
Track net displacement on North-South and East-West axes separately to determine the relative final position.
Coordinate Mapping
Set Point A at (0, 0). Movement 1: North 6km (+6 Y). Movement 2: Right turn East 2km (+2 X). Movement 3: Left turn North 3km (+3 Y). Movement 4: Left turn West 7km (-7 X). Movement 5: Left turn South 9km (-9 Y).
Net Displacement Calculation
Final X = 2 - 7 = -5 (5 km West of point A). Final Y = 6 + 3 - 9 = 0 (Same horizontal level as point A). Dilip is currently at 5 km West relative to point A.
Final Direction Determination
Since Dilip is 5 km West of point A, to return to Point A, he must travel 5 km towards the East.
A: This is his current position relative to A, not the direction required to return. B: Calculation of East-West movement results in 5km, not 3km. D: This represents his current displacement from A, not the direction he needs to travel to reach A.
C is correct because the net displacement is 5 km West of the starting point, requiring a 5 km movement to the East to return to Point A.
When solving direction problems with many turns, always convert them to North/South/East/West vectors first to avoid confusion caused by visual path drawing.
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