# Strolling in the Cartesian plane

Geometry Level 2

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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