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Natesh starts from point Y and drives 58 km towards East. He then takes a left turn, drives 28 km, turns left and drives 40 km. He then takes a left turn and drives 71 km. He takes a right turn, drives 18 km to stop at point Z. How far (shortest distance) and towards which direction should he drive in order to reach point Y again? (All turns are 90-degree turns only unless specified.)
43 km towards north
45 km towards west
39 km towards south
41 km towards north
43 km towards north
Calculate final net displacement by treating East/West as X-axis and North/South as Y-axis. Point Y is at (0,0), find the final coordinate of Z and reverse it.
Calculate final net displacement by treating East/West as X-axis and North/South as Y-axis. Point Y is at (0,0), find the final coordinate of Z and reverse it.
Mapping the path on a Cartesian Plane
Start at Y(0,0). Move East 58 km to (58,0). Turn left (North) 28 km to (58,28). Turn left (West) 40 km to (18,28). Turn left (South) 71 km to (18,-43). Turn right (West) 18 km to point Z(0,-43).
Determining displacement
Point Z is at (0, -43). Point Y is at (0,0). To reach Y from Z(0, -43), one must move 0 km East/West and 43 km North.
B: Incorrect, the horizontal displacement is 0, not 45. C: Incorrect, moving south would take the user further away from Y(0,0). D: Incorrect, calculation shows exactly 43 km, not 41.
A is correct because the final coordinate of point Z is (0, -43) relative to Y(0,0), necessitating a 43 km movement in the positive Y direction (North) to return to the origin.
In any direction problem involving multiple turns, always use +X for East, -X for West, +Y for North, and -Y for South to avoid visual clutter and logical errors.
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