To find the coordinates of the midpoint of the line segment [tex]\(\overline{AS}\)[/tex] with endpoints [tex]\(A(-4,7)\)[/tex] and [tex]\(S(5,3)\)[/tex], we can use the midpoint formula. The midpoint formula states that the midpoint, [tex]\(M\)[/tex], of a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Let's apply this formula step-by-step to our given points [tex]\(A(-4, 7)\)[/tex] and [tex]\(S(5, 3)\)[/tex]:
1. Calculate the x-coordinate of the midpoint:
[tex]\[
M_x = \frac{-4 + 5}{2}
= \frac{1}{2}
\][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[
M_y = \frac{7 + 3}{2}
= \frac{10}{2}
= 5
\][/tex]
Therefore, the coordinates of the midpoint are:
[tex]\[ M = \left(\frac{1}{2}, 5\right) \][/tex]
Thus, the correct choice is (C) (or (D) if you consider different formatting).
