4) \( A \) line segment has the endpoints \( B(8,6) \) and \( C(10,4) \). Find the coordinates of its midpoint \( M \). (1) Write the coordinates as decimals or integers. \( M= \)

To find the midpoint \( M \) of a line segment with endpoints \( B(x_1, y_1) \) and \( C(x_2, y_2) \), we use the midpoint formula: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] For the endpoints \( B(8, 6) \) and \( C(10, 4) \): - \( x_1 = 8 \) - \( y_1 = 6 \) - \( x_2 = 10 \) - \( y_2 = 4 \) Now, we can substitute these values into the midpoint formula: \[ M = \left( \frac{8 + 10}{2}, \frac{6 + 4}{2} \right) \] Calculating the x-coordinate: \[ \frac{8 + 10}{2} = \frac{18}{2} = 9 \] Calculating the y-coordinate: \[ \frac{6 + 4}{2} = \frac{10}{2} = 5 \] Thus, the coordinates of the midpoint \( M \) are: \[ M = (9, 5) \] So, the final answer is: \[ M = (9, 5) \]