To find the midpoint of the line segment connecting two points [tex]\( A \)[/tex] and [tex]\( B \)[/tex], we use the midpoint formula. The midpoint formula is given by:
[tex]\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
where [tex]\((x_1, y_1)\)[/tex] are the coordinates of point [tex]\(A\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of point [tex]\(B\)[/tex].
Given:
[tex]\[ A = (-3, -5) \][/tex]
[tex]\[ B = (2, 5) \][/tex]
Let's identify the coordinates:
[tex]\[ x_1 = -3, \quad y_1 = -5 \][/tex]
[tex]\[ x_2 = 2, \quad y_2 = 5 \][/tex]
We now substitute these coordinates into the midpoint formula:
1. Calculate the x-coordinate of the midpoint:
[tex]\[
\frac{x_1 + x_2}{2} = \frac{-3 + 2}{2} = \frac{-1}{2} = -0.5
\][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[
\frac{y_1 + y_2}{2} = \frac{-5 + 5}{2} = \frac{0}{2} = 0
\][/tex]
Therefore, the coordinates of the midpoint are:
[tex]\[
(-0.5, 0)
\][/tex]
So, the midpoint of the line segment [tex]\(\overline{A B}\)[/tex] is [tex]\( \boxed{(-0.5, 0)} \)[/tex].
