Answer :
To find the midpoint of a line segment with endpoints [tex]\( G(-7, 3) \)[/tex] and [tex]\( H(1, -2) \)[/tex], we use the midpoint formula. The midpoint formula is:
[tex]\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
where [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] are the coordinates of the endpoints.
Let's plug in the coordinates for [tex]\( G \)[/tex] and [tex]\( H \)[/tex]:
1. Calculate the x-coordinate of the midpoint:
[tex]\[ x = \frac{-7 + 1}{2} \][/tex]
[tex]\[ x = \frac{-6}{2} \][/tex]
[tex]\[ x = -3 \][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[ y = \frac{3 + (-2)}{2} \][/tex]
[tex]\[ y = \frac{3 - 2}{2} \][/tex]
[tex]\[ y = \frac{1}{2} \][/tex]
Therefore, the midpoint of [tex]\( \overline{GH} \)[/tex] is:
[tex]\[ \left( -3, \frac{1}{2} \right) \][/tex]
So the correct answer is:
A. [tex]\( \left( -3, \frac{1}{2} \right) \)[/tex]
[tex]\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
where [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] are the coordinates of the endpoints.
Let's plug in the coordinates for [tex]\( G \)[/tex] and [tex]\( H \)[/tex]:
1. Calculate the x-coordinate of the midpoint:
[tex]\[ x = \frac{-7 + 1}{2} \][/tex]
[tex]\[ x = \frac{-6}{2} \][/tex]
[tex]\[ x = -3 \][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[ y = \frac{3 + (-2)}{2} \][/tex]
[tex]\[ y = \frac{3 - 2}{2} \][/tex]
[tex]\[ y = \frac{1}{2} \][/tex]
Therefore, the midpoint of [tex]\( \overline{GH} \)[/tex] is:
[tex]\[ \left( -3, \frac{1}{2} \right) \][/tex]
So the correct answer is:
A. [tex]\( \left( -3, \frac{1}{2} \right) \)[/tex]
