A problem in my book shows that:

$\displaystyle \sqrt{({x_2 - \frac{x_1 + x_2}{2})^{2} + (y_2 - \frac{y_1 + y_2}{2}})^{2}} = \frac{1}{2}\sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}}\$

But I don't understand how they got this. This is what I have so far:

$\displaystyle \sqrt{({x_2 - \frac{x_1 + x_2}{2})^{2} + (y_2 - \frac{y_1 + y_2}{2}})^{2}} = \sqrt{({\frac{2x_2}{2} - \frac{x_1 + x_2}{2})^{2} + (\frac{2y_2}{2} - \frac{y_1 + y_2}{2}})^{2}} = \sqrt{({\frac{-x_1 + 3x_2}{2})^{2} + (\frac{-y_1 + 3y_2}{2}})^{2}}$

What do I do now?