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