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Yes displacemnt is independent of path...like displacemt on triangular path will be hypotenuse..on circular it will be diameter,,,so it doesnot depend on path..

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Displacement is defined as the shortest distance from mean position to other extreme position 
so if u are going on a rectangular path 
u might go along the sides from one opposite CORNER to other 
u might go diagonally 

in both the cases displacement is equal to the length of diagonal[as it is the shortest path] 

hence proved that it is independent of path
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