Strolling in the Cartesian plane

Geometry Level 3

Suppose you are standing at the coordinates \((0,0)\). You have been instructed to move to the coordinates \((a,b)\), but instead you move to the coordinates \((b,a)\). How far are you from your destination?

The distance can be expressed as \(|a-b| \sqrt c\) (here, \(a\) and \(b\) are the same as used above and \(c\) is square-free).

What is the value of \(c\)?

\(\text{Note:} a\neq b\)


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