To find the midpoint of a line segment given the endpoints, we use the midpoint formula. The midpoint [tex]\( M \)[/tex] of a line segment with endpoints [tex]\( G(x_1, y_1) \)[/tex] and [tex]\( H(x_2, y_2) \)[/tex] is given by the formula:
[tex]\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
For the endpoints [tex]\( G(-7, 3) \)[/tex] and [tex]\( H(1, -2) \)[/tex], we can identify:
- [tex]\( x_1 = -7 \)[/tex]
- [tex]\( y_1 = 3 \)[/tex]
- [tex]\( x_2 = 1 \)[/tex]
- [tex]\( y_2 = -2 \)[/tex]
Now, we substitute these coordinates into the midpoint formula:
1. Calculate the x-coordinate of the midpoint:
[tex]\[
\frac{x_1 + x_2}{2} = \frac{-7 + 1}{2} = \frac{-6}{2} = -3
\][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[
\frac{y_1 + y_2}{2} = \frac{3 + (-2)}{2} = \frac{3 - 2}{2} = \frac{1}{2}
\][/tex]
Therefore, the midpoint of [tex]\( \overline{GH} \)[/tex] is:
[tex]\[
\left( -3, \frac{1}{2} \right)
\][/tex]
The correct answer is:
A. [tex]\(\left(-3, \frac{1}{2}\right)\)[/tex]
