To find the midpoint of the line segment [tex]\(\overline{GH}\)[/tex], we use the midpoint formula. The midpoint formula between two points [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]
Given the points [tex]\( G(14, 3) \)[/tex] and [tex]\( H(10, -6) \)[/tex]:
1. First, find the x-coordinate of the midpoint by adding the x-coordinates of [tex]\( G \)[/tex] and [tex]\( H \)[/tex], then dividing by 2:
[tex]\[ \frac{14 + 10}{2} = \frac{24}{2} = 12.0 \][/tex]
2. Next, find the y-coordinate of the midpoint by adding the y-coordinates of [tex]\( G \)[/tex] and [tex]\( H \)[/tex], then dividing by 2:
[tex]\[ \frac{3 + (-6)}{2} = \frac{-3}{2} = -1.5 \][/tex]
Therefore, the midpoint of [tex]\( \overline{GH} \)[/tex] is [tex]\( \left( 12.0, -1.5 \right) \)[/tex].
The correct answer is:
C. [tex]\( \left(12, -\frac{3}{2} \right) \)[/tex]
