Answer
$\sqrt{2a^{2}-4ab+2b^{2}} $
Work Step by Step
To find the distance between $(a,b)$ and $(b,a)$,
we use the distance formula: $d=\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$.
We plug in the given $x$ and $y$ values: $d=\sqrt {(b-a)^{2}+(a-b)^{2}}$.
We then simplify to arrive at the answer: $d=\sqrt {b^{2}-2ab+a^{2}+a^{2}-2ab+b^{2}}=\sqrt {2a^{2}-4ab+2b^{2}} $.