To determine the midpoint of the line segment [tex]\(\overline{GH}\)[/tex] with endpoints [tex]\(G(-7, 3)\)[/tex] and [tex]\(H(1, -2)\)[/tex], we use the midpoint formula:
[tex]\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Here, [tex]\((x_1, y_1) = (-7, 3)\)[/tex] and [tex]\((x_2, y_2) = (1, -2)\)[/tex].
1. Calculate the [tex]\(x\)[/tex]-coordinate of the midpoint:
[tex]\[ \frac{-7 + 1}{2} = \frac{-6}{2} = -3 \][/tex]
2. Calculate the [tex]\(y\)[/tex]-coordinate of the midpoint:
[tex]\[ \frac{3 + (-2)}{2} = \frac{3 - 2}{2} = \frac{1}{2} \][/tex]
So, the coordinates of the midpoint of [tex]\(\overline{GH}\)[/tex] are:
[tex]\[ \left( -3, \frac{1}{2} \right) \][/tex]
Therefore, the correct answer is:
A. [tex]\(\left(-3, \frac{1}{2}\right)\)[/tex]
