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Pranit starts from Point A and drives 27 km towards West. He then takes a left turn, drives 17 km, turns left and drives 14 km. He then takes a left turn and drives 10 km. He takes a final right turn, drives 13 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.)
7 km towards South
7 km towards North
5 km towards North
5 km towards South
7 km towards North
Track horizontal (X) and vertical (Y) displacements independently. East/West cancel/add X, North/South cancel/add Y.
Track horizontal (X) and vertical (Y) displacements independently. East/West cancel/add X, North/South cancel/add Y.
Coordinate Mapping
Set Point A as (0, 0). Move 27 West (-27, 0). Left turn (South)тВБтВЗkm тЖТ (-27, -17). Left turn (East)тВБтВДkm тЖТ (-13, -17). Left turn (North)тВБтВАkm тЖТ (-13, -7). Right turn (East)тВБтВГkm тЖТ (0, -7). Wait, recalculating turns: A(0,0) тЖТ West 27 to (-27,0) тЖТ Left (South)тВБтВЗ to (-27,-17) тЖТ Left (East)тВБтВД to (-13,-17) тЖТ Left (North)тВБтВА to (-13,-7) тЖТ Right (East)тВБтВГ to (0,-7).
Net Displacement
Final position P is (0, -7) relative to A(0, 0). To reach A from (0, -7), we need to move 0 units in X and +7 units in Y (North). Wait, let's re-verify directions: Start West, Left is South, Left is East, Left is North, Right is East. Final position is (0,-7). Therefore, one must go 7km towards North to return to A.
A: 7km South would take him further from origin. C: 5km North is incorrect distance. D: 5km South is incorrect distance and direction.
B is correct because the net coordinate calculation starting from origin (0,0) results in Point P at (0, -7), which is 7km South of Point A, meaning he must travel 7km North to return.
When tracking directions, always draw a small plus-sign axis (N/S/E/W) and treat turns as rotation: Left = -90 deg, Right = +90 deg relative to current heading.
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