A $200\mathrm{g}$ mass is at (0, 0), a $300\mathrm{g}$ mass is at ($10\mathrm{cm}$, 0), and a $400\mathrm{g}$ mass is at ($13\mathrm{cm}$, $15\mathrm{cm}$). What are the coordinates of the center of mass?

Use the formula for the x-coordinate of the center of mass: x_cm = (m1 * x1 + m2 * x2 + m3 * x3) / (m1 + m2 + m3). Substitute the values: x_cm = (0.2 * 0 + 0.3 * 10 + 0.4 * 13) / (0.2 + 0.3 + 0.4).

Use the formula for the y-coordinate of the center of mass: y_cm = (m1 * y1 + m2 * y2 + m3 * y3) / (m1 + m2 + m3). Substitute the values: y_cm = (0.2 * 0 + 0.3 * 0 + 0.4 * 15) / (0.2 + 0.3 + 0.4).