Let's find the **y-coordinate of the center of mass** for the system. ### Step 1: Write the formula for the y-coordinate of the center of mass \[ y_{cm} = \frac{\sum m_i y_i}{\sum m_i} \] ### Step 2: List the masses and their y-coordinates - \( m_1 = 5, \quad y_1 = 1 \) - \( m_2 = 4, \quad y_2 = 5 \) - \( m_3 = 3, \quad y_3 = 2 \) - \( m_4 = 6, \quad y_4 = -2 \) ### Step 3: Calculate the numerator \(\sum m_i y_i\) \[ m_1y_1 + m_2y_2 + m_3y_3 + m_4y_4 = (5 \times 1) + (4 \times 5) + (3 \times 2) + (6 \times -2) \] \[ = 5 + 20 + 6 - 12 = 19 \] ### Step 4: Calculate the denominator \(\sum m_i\) \[ m_1 + m_2 + m_3 + m_4 = 5 + 4 + 3 + 6 = 18 \] ### Step 5: Plug into the formula \[ y_{cm} = \frac{19}{18} \] --- ### **Final Answer** \[ \boxed{\frac{19}{18}} \]

The y-coordinate of the center of mass is obtained by taking the weighted average of the y-coordinates of all masses, with weights proportional to their masses. This ensures the point reflects the distribution of mass along the y-axis, considering each mass's position.