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Brinda starts from Point A and drives 19┬аkm towards West. She then takes a left turn, drives 22┬аkm, turns left and drives 25┬аkm. She takes a final left turn, drives 22┬аkm and stops at Point P. How far (shortest distance) and towards which direction should she drive to reach Point A again? (All turns are 90 degrees turns only unless specified.)
7┬аkm towards the West
7┬аkm towards the South
6┬аkm towards the West
6┬аkm towards the East
6┬аkm towards the West
Track movements along the Cartesian coordinate system: X-axis for East/West and Y-axis for North/South. Balance opposing movements to find the net displacement quickly.
Track movements along the Cartesian coordinate system: X-axis for East/West and Y-axis for North/South. Balance opposing movements to find the net displacement quickly.
Step 1: Start at Point A and move West
Brinda starts from Point A and drives 19 km towards West. Position becomes 19 km West of A.
Step 2: First Left turn (South) and second Left turn (East)
She takes a left turn (facing South) and drives 22 km. Then she takes another left turn (facing East) and drives 25 km.
Step 3: Final Left turn (North) to Point P
She takes a final left turn (facing North), drives 22 km, and stops at Point P. The northward movement of 22 km cancels out the earlier southward movement of 22 km.
Step 4: Distance and Direction to return to Point A
Total horizontal distance from A is 19 km + 25 km = 44 km West. Therefore, to reach Point A from Point P, she must drive 44 km towards the East.
A: 7 km towards West is incorrect as horizontal distance is cumulative (19 + 25 = 44 km). B: 7 km towards South is incorrect as vertical displacements cancel out (22 South - 22 North = 0). D: 6 km towards East is an incorrect calculation.
C is correct because Brinda's net position relative to Point A is 44 km West, requiring her to travel 44 km towards the East to return to Point A.
In multi-turn navigation problems, always track orthogonal movements (North-South and East-West) separately. Opposite directions subtract directly.
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