To find the midpoint of the line segment \(\overline{GH}\), we use the midpoint formula. The formula for the midpoint, \(M\), between two points \(G(x_1, y_1)\) and \(H(x_2, y_2)\) in a coordinate plane is given by:
[tex]\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Given the endpoints \(G(14, 3)\) and \(H(10, -6)\), let's identify the coordinates clearly:
- \(G\) has coordinates \((x_1, y_1) = (14, 3)\)
- \(H\) has coordinates \((x_2, y_2) = (10, -6)\)
We substitute these coordinates into the midpoint formula:
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]
Therefore, the coordinates of the midpoint \(M\) are:
[tex]\[
M = \left(12, -1.5\right)
\][/tex]
The correct answer is:
C. [tex]\(\left(12, -\frac{3}{2}\right)\)[/tex]
