\begin{tabular}{|l|}\hline Directions: Find the coordinates of the midpoint \\ \hline 6. \( A(5,8) \) and \( B(-1,-4) \) \\ \\ \hline\end{tabular}

To find the coordinates of the midpoint \( M \) of the line segment connecting points \( A(5,8) \) and \( B(-1,-4) \), we can use the midpoint formula: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] where \( (x_1, y_1) \) are the coordinates of point \( A \) and \( (x_2, y_2) \) are the coordinates of point \( B \). Substituting the coordinates of points \( A \) and \( B \): - \( A(5, 8) \) gives us \( x_1 = 5 \) and \( y_1 = 8 \) - \( B(-1, -4) \) gives us \( x_2 = -1 \) and \( y_2 = -4 \) Now, we can calculate the midpoint: \[ M = \left( \frac{5 + (-1)}{2}, \frac{8 + (-4)}{2} \right) \] Calculating the x-coordinate: \[ \frac{5 - 1}{2} = \frac{4}{2} = 2 \] Calculating the y-coordinate: \[ \frac{8 - 4}{2} = \frac{4}{2} = 2 \] Thus, the coordinates of the midpoint \( M \) are: \[ M(2, 2) \] So, the final answer is: \[ \text{Midpoint } M(2, 2) \]