To find the coordinates of the midpoint of the line segment [tex]\(\overline{BC}\)[/tex] with endpoints [tex]\(B(5,9)\)[/tex] and [tex]\(C(-4,-3)\)[/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]
Here, [tex]\((x_1, y_1)\)[/tex] are the coordinates of point [tex]\(B\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of point [tex]\(C\)[/tex]. So, we have:
[tex]\[
(x_1, y_1) = (5, 9) \quad \text{and} \quad (x_2, y_2) = (-4, -3)
\][/tex]
Substitute these values into the midpoint formula:
[tex]\[
\text{Midpoint} = \left( \frac{5 + (-4)}{2}, \frac{9 + (-3)}{2} \right)
\][/tex]
Calculate each part separately:
1. For the x-coordinate:
[tex]\[
\frac{5 + (-4)}{2} = \frac{5 - 4}{2} = \frac{1}{2} = 0.5
\][/tex]
2. For the y-coordinate:
[tex]\[
\frac{9 + (-3)}{2} = \frac{9 - 3}{2} = \frac{6}{2} = 3
\][/tex]
So, the coordinates of the midpoint are:
[tex]\[
(0.5, 3)
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{(0.5, 3)}
\][/tex]
