To find the midpoint of a line segment defined by two endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], we use the midpoint formula. The formula for the midpoint [tex]\((M_x, M_y)\)[/tex] of the line segment is:
[tex]\[
M_x = \frac{x_1 + x_2}{2}
\][/tex]
[tex]\[
M_y = \frac{y_1 + y_2}{2}
\][/tex]
Given the endpoints are [tex]\((8, -3)\)[/tex] and [tex]\((-5, -9)\)[/tex], we can substitute these values into the formula:
[tex]\[
M_x = \frac{8 + (-5)}{2} = \frac{8 - 5}{2} = \frac{3}{2} = 1.5
\][/tex]
[tex]\[
M_y = \frac{-3 + (-9)}{2} = \frac{-3 - 9}{2} = \frac{-12}{2} = -6
\][/tex]
Therefore, the coordinates of the midpoint are [tex]\((1.5, -6)\)[/tex].
The correct answer is:
D. [tex]\((1.5, -6)\)[/tex]
