#### Answer

$\overline{x}=\dfrac{a}{3}$ and $\overline{y}=\dfrac{a}{3}$

#### Work Step by Step

We have a triangle with vertices $(0,0), (a,0), (0,a)$ 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 $(0,a)$, which corresponds to the $x$-axis.
Therefore, the center of mass is:
$\overline{x}=\dfrac{a}{3}$ and $\overline{y}=\dfrac{a}{3}$