To find the midpoint of a line segment with endpoints [tex]\( G(-3,7) \)[/tex] and [tex]\( H(-3,-7) \)[/tex], we use the midpoint formula:
[tex]\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
where [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] are the coordinates of the endpoints. In this case, [tex]\( G \)[/tex] has coordinates [tex]\((-3, 7)\)[/tex] and [tex]\( H \)[/tex] has coordinates [tex]\((-3, -7)\)[/tex].
1. Calculate the x-coordinate of the midpoint:
[tex]\[ \frac{-3 + (-3)}{2} = \frac{-3 - 3}{2} = \frac{-6}{2} = -3 \][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[ \frac{7 + (-7)}{2} = \frac{7 - 7}{2} = \frac{0}{2} = 0 \][/tex]
Therefore, the coordinates of the midpoint of [tex]\(\overline{GH}\)[/tex] are:
[tex]\[ (-3, 0) \][/tex]
Among the provided options, the correct coordinates of the midpoint of [tex]\(\overline{GH}\)[/tex] are:
[tex]\[ (-3, 0) \][/tex]
