To determine the midpoint of a line segment with given endpoints [tex]\((-6, -3)\)[/tex] and [tex]\( (9, -7)\)[/tex], we use the midpoint formula. The midpoint of a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
In this case, the coordinates of the endpoints are:
- [tex]\(x_1 = -6\)[/tex]
- [tex]\(y_1 = -3\)[/tex]
- [tex]\(x_2 = 9\)[/tex]
- [tex]\(y_2 = -7\)[/tex]
Now, we substitute these values into the midpoint formula:
[tex]\[
\text{Midpoint}_x = \frac{-6 + 9}{2}
\][/tex]
[tex]\[
\text{Midpoint}_x = \frac{3}{2}
\][/tex]
[tex]\[
\text{Midpoint}_x = 1.5
\][/tex]
Next, we find the midpoint's y-coordinate:
[tex]\[
\text{Midpoint}_y = \frac{-3 + (-7)}{2}
\][/tex]
[tex]\[
\text{Midpoint}_y = \frac{-10}{2}
\][/tex]
[tex]\[
\text{Midpoint}_y = -5
\][/tex]
Hence, the coordinates of the midpoint are:
[tex]\[
(1.5, -5)
\][/tex]
So, the correct answer is:
C. [tex]\((1.5, -5)\)[/tex]
