Answer
$\overline{x}=\dfrac{1}{3}$ and $\overline{y}=\dfrac{1}{3}$
Work Step by Step
We have a triangle with vertices $(0,0), (1,0), (0,1)$ whose x- co-ordinate is $0$, which is a third of $(1,0)$ from the edge that corresponds to the $y$-axis.
Also, the y-coordinate is a third of the distance of $(0,1)$, which corresponds to $X$-axis.
Therefore, the center of mass is:
$\overline{x}=\dfrac{1}{3}$ and $\overline{y}=\dfrac{1}{3}$
