To find the midpoint of a line segment, we use the midpoint formula. The midpoint of a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
In this problem, the endpoints of the segment [tex]\(\overline{GH}\)[/tex] are [tex]\(G (-7, 3)\)[/tex] and [tex]\(H (1, -2)\)[/tex].
Let's apply the formula step-by-step:
1. Calculate the x-coordinate of the midpoint:
[tex]\[
\text{midpoint}_x = \frac{x_1 + x_2}{2} = \frac{-7 + 1}{2} = \frac{-6}{2} = -3
\][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[
\text{midpoint}_y = \frac{y_1 + y_2}{2} = \frac{3 - 2}{2} = \frac{1}{2}
\][/tex]
So, the coordinates of the midpoint are [tex]\(\left( -3, \frac{1}{2} \right)\)[/tex].
Comparing this with the given options, we see that the correct choice is:
A. [tex]\(\left( -3, \frac{1}{2} \right)\)[/tex].
