Answer
$\overline{x}=\dfrac{a}{3}$ and $\overline{y}=\dfrac{b}{3}$
Work Step by Step
We notice that the triangle with vertices $(0,0), (a,0), (0,b)$ has the x-coordinate a third of the distance $(a,0)$ from the edge, which corresponds to the $y$-axis.
Also, the y-coordinate is a third of the distance of $(0,b)$, which corresponds to the $x$-axis.
This means that $\overline{x}=\dfrac{a}{3}$ and $\overline{y}=\dfrac{b}{3}$
