Answer
$\overline{x}=\dfrac{a}{2}$ and $\overline{y}=\dfrac{b}{3}$
Work Step by Step
We notice that the triangle with vertices $(0,0), (a,0), (\dfrac{a}{2},b)$ has the x-coordinate of the center of mass equal to $\dfrac{a}{2}$ and is symmetric about the line $x =\dfrac{a}{2}$.
Also, the y-coordinate is a third of the distance of $(\dfrac{a}{2},b)$, which corresponds to the $x$-axis.
This means that $\overline{x}=\dfrac{a}{2}$ and $\overline{y}=\dfrac{b}{3}$
