To find the midpoint of a line segment with endpoints [tex]\( G(14, 3) \)[/tex] and [tex]\( H(10, -6) \)[/tex], we can use the midpoint formula. The midpoint formula is:
[tex]\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Here, the coordinates of [tex]\( G \)[/tex] are [tex]\( (x_1, y_1) = (14, 3) \)[/tex] and the coordinates of [tex]\( H \)[/tex] are [tex]\( (x_2, y_2) = (10, -6) \)[/tex].
1. Calculate the x-coordinate of the midpoint:
[tex]\[
\frac{x_1 + x_2}{2} = \frac{14 + 10}{2} = \frac{24}{2} = 12
\][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[
\frac{y_1 + y_2}{2} = \frac{3 + (-6)}{2} = \frac{3 - 6}{2} = \frac{-3}{2} = -1.5
\][/tex]
Thus, the midpoint of [tex]\(\overline{GH}\)[/tex] is:
[tex]\[
\left( 12, -1.5 \right)
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{\left(12, -\frac{3}{2}\right)}
\][/tex]
Therefore, the answer is:
C. [tex]\(\left(12, -\frac{3}{2}\right)\)[/tex]
