# Appendix B - Coordinate Geometry and Lines - B Exercises: 6

$d=\sqrt {2a^{2}-4ab+2b^{2}}$

#### 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, $d=\sqrt {2a^{2}-4ab+2b^{2}}$

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