jmc

There are two segments of Brenda's trip: from $(-4,5)$ to $(0,0)$, and from $(0,0)$ to $(5,-4)$. Using the distance formula, the total distance is $$\begin{array}{rl}\sqrt{(-4-0{)}^2+(5-0{)}^2}& +\sqrt{(5-0{)}^2+(-4-0{)}^2}\\ & =\sqrt{16+25}+\sqrt{25+16}\\ & =\boxed{2\sqrt{41}}.\end{array}$$