To find the midpoint of a line segment with endpoints [tex]\( G(14, 3) \)[/tex] and [tex]\( H(10, -6) \)[/tex], you can use the midpoint formula. The midpoint formula for the endpoints [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] is:
[tex]\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
In this problem, the coordinates of points [tex]\( G \)[/tex] and [tex]\( H \)[/tex] are:
[tex]\( G(14, 3) \)[/tex] and [tex]\( H(10, -6) \)[/tex].
To find the x-coordinate of the midpoint:
[tex]\[
\frac{x_1 + x_2}{2} = \frac{14 + 10}{2} = \frac{24}{2} = 12
\][/tex]
To find the y-coordinate of the midpoint:
[tex]\[
\frac{y_1 + y_2}{2} = \frac{3 + (-6)}{2} = \frac{3 - 6}{2} = \frac{-3}{2} = -\frac{3}{2}
\][/tex]
Thus, the coordinates of the midpoint of [tex]\(\overline{GH}\)[/tex] are:
[tex]\[
\left( 12, -\frac{3}{2} \right)
\][/tex]
From the answer choices given:
A. [tex]\((6, -15)\)[/tex]
B. [tex]\(\left(-2, -\frac{9}{2}\right)\)[/tex]
C. [tex]\(\left(12, -\frac{3}{2}\right)\)[/tex]
D. [tex]\((24, -3)\)[/tex]
E. [tex]\((18, 12)\)[/tex]
The correct answer is:
[tex]\[
C. \left(12, -\frac{3}{2}\right)
\][/tex]
