To find the midpoint [tex]\( M \)[/tex] of the line segment [tex]\(\overline{AB}\)[/tex], where [tex]\( A = (2, 5) \)[/tex] and [tex]\( B = (-6, -3) \)[/tex], we use the midpoint formula. The midpoint [tex]\( M \)[/tex] of a segment with endpoints [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] is given by:
[tex]\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Given the coordinates of point [tex]\( A \)[/tex] as [tex]\( (2, 5) \)[/tex] and point [tex]\( B \)[/tex] as [tex]\( (-6, -3) \)[/tex], we substitute these values into the formula:
1. Calculate the x-coordinate of the midpoint:
[tex]\[
\text{midpoint}_x = \frac{x_1 + x_2}{2} = \frac{2 + (-6)}{2} = \frac{2 - 6}{2} = \frac{-4}{2} = -2
\][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[
\text{midpoint}_y = \frac{y_1 + y_2}{2} = \frac{5 + (-3)}{2} = \frac{5 - 3}{2} = \frac{2}{2} = 1
\][/tex]
Therefore, the coordinates of the midpoint [tex]\( M \)[/tex] are:
[tex]\[
M = (-2, 1)
\][/tex]
