To find the midpoint [tex]\( M \)[/tex] of the line segment [tex]\( \overline{AB} \)[/tex] with endpoints [tex]\( A = (2, 5) \)[/tex] and [tex]\( B = (-6, -3) \)[/tex], we can use the midpoint formula:
[tex]\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
where [tex]\((x_1, y_1) \)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of points [tex]\( A \)[/tex] and [tex]\( B \)[/tex] respectively.
### Step-by-Step Solution:
1. Identify the coordinates:
For point [tex]\( A \)[/tex]:
[tex]\[
x_1 = 2, \quad y_1 = 5
\][/tex]
For point [tex]\( B \)[/tex]:
[tex]\[
x_2 = -6, \quad y_2 = -3
\][/tex]
2. Plug the coordinates into the midpoint formula for the x-coordinate:
[tex]\[
\frac{x_1 + x_2}{2} = \frac{2 + (-6)}{2} = \frac{2 - 6}{2} = \frac{-4}{2} = -2.0
\][/tex]
3. Plug the coordinates into the midpoint formula for the y-coordinate:
[tex]\[
\frac{y_1 + y_2}{2} = \frac{5 + (-3)}{2} = \frac{5 - 3}{2} = \frac{2}{2} = 1.0
\][/tex]
### Putting it together:
Therefore, the midpoint [tex]\( M \)[/tex] of [tex]\( \overline{AB} \)[/tex] is:
[tex]\[
M = (-2.0, 1.0)
\][/tex]
Thus, the coordinates of the midpoint [tex]\( M \)[/tex] are:
[tex]\(
M = (-2.0, 1.0)
\)[/tex]
