Answer
$\overline{x}=\dfrac{a}{2}; \overline{y}=\dfrac{b}{3}$
Work Step by Step
It has been seen that a triangle has vertices $(0,0), (a,0), (\dfrac{a}{2},b)$, whose x-coordinate of the center of mass is $\dfrac{a}{2}$ and which 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 $x$-axis.
Therefore, the center of mass is:
$\overline{x}=\dfrac{a}{2} ;\overline{y}=\dfrac{b}{3}$
