Answer
$\overline{x}=\dfrac{M_y}{M}$ and $\overline{y}=\dfrac{M_x}{M}$
Work Step by Step
Let $\overline{x}$ and $\overline{y}$ be the center of mass of a thin plate of material. This can be mathematically expressed as:
$\overline{x}=\dfrac{M_y}{M}$ and $\overline{y}=\dfrac{M_x}{M}$
where $M \to \int dm ; \\ M_x \to \int (y) dm \\ M_y \to \int (x) dm$
