Answer
$d=\sqrt {2a^{2}-4ab+2b^{2}}$
Work Step by Step
Use distance formula $d=\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$ to find the distance between $(a,b),(b,a)$
Plug into the values of $x$ and $y$.
$d=\sqrt {(b-a)^{2}+(a-b)^{2}}$
We need to simplify to arrive at the answer .
$d=\sqrt {b^{2}+a^{2}-2ab+a^{2}+b^{2}-2ab}$
Hence, $d=\sqrt {2a^{2}-4ab+2b^{2}}$
