Answer
$\overline{x}=\dfrac{a}{3}; \overline{y}=\dfrac{b}{3}$
Work Step by Step
We have a triangle with vertices $(0,0), (a,0), (0,b)$ whose x-coordinate corresponds to a third of the distance $(a,0)$ from the edge at the $y$-axis.
Also, the y-coordinate is a third of the distance of $(0,b)$, which corresponds to the $x$-axis.
Therefore, the center of mass is:
$\overline{x}=\dfrac{a}{3}; \overline{y}=\dfrac{b}{3}$
