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Priyanshu starts from Point A and drives 17 km towards the south. He then takes a right turn, drives 12 km, turns right and drives 24 km. He then takes a right turn and drives 19 km. He takes a final right turn, drives 7 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.)
9 km to the east
9 km to the west
7 km to the west
7 km to the east Question ID : 4410091567499 Option 1 ID : 4410096191311 Option 2 ID : 4410096191310 Option 3 ID : 4410096191309 Option 4 ID : 4410096191308 Status : Answered Chosen Option : C
7 km to the west
Represent movements on a coordinate plane starting at (0,0) and sum the net X and Y displacements; the shortest distance to return is the additive inverse of the final position.
Represent movements on a coordinate plane starting at (0,0) and sum the net X and Y displacements; the shortest distance to return is the additive inverse of the final position.
Calculate movement in coordinate system
Start at (0,0). South 17: (0, -17). Right (West) 12: (-12, -17). Right (North) 24: (-12, 7). Right (East) 19: (7, 7). Final Right (South) 7: (7, 0).
Determine net displacement
Priyanshu is currently at point (7, 0) relative to start point A(0, 0). This means he is 7 km East of A.
Calculate path back to A
To return from (7, 0) to (0, 0), he must move 7 units in the negative X direction (West). Thus, he needs to drive 7 km to the west.
A: 9 km to the east takes him further away from point A. B: 9 km to the west is numerically incorrect based on the final coordinate calculations. D: 7 km to the east moves him to 14 km away from point A instead of back to it.
C is correct because Priyanshu's final position is 7 km East of Point A, requiring a 7 km move to the West to return.
In multi-turn direction problems, always keep track of the cumulative movement along X (East/West) and Y (North/South) axes separately to prevent errors.
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