To find the midpoint \( M \) of a line segment with endpoints \( V(x_1, y_1) \) and \( W(x_2, y_2) \), we can use the midpoint formula:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Given the endpoints \( V(1, 75) \) and \( W(71, 77) \):
- \( x_1 = 1 \)
- \( y_1 = 75 \)
- \( x_2 = 71 \)
- \( y_2 = 77 \)
Now, substitute these values into the midpoint formula:
\[ M = \left( \frac{1 + 71}{2}, \frac{75 + 77}{2} \right) \]
Calculating the x-coordinate:
\[ \frac{1 + 71}{2} = \frac{72}{2} = 36 \]
Calculating the y-coordinate:
\[ \frac{75 + 77}{2} = \frac{152}{2} = 76 \]
Thus, the coordinates of the midpoint \( M \) are:
\[ M(36, 76) \]