To find the midpoint of a line segment with given endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], we use the midpoint formula. The midpoint [tex]\((M)\)[/tex] is given by:
[tex]\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Given the endpoints [tex]\((-6, -3)\)[/tex] and [tex]\(9, -7\)[/tex]:
Step-by-Step Solution:
1. Identify the coordinates of the endpoints:
- [tex]\((x_1, y_1) = (-6, -3)\)[/tex]
- [tex]\((x_2, y_2) = (9, -7)\)[/tex]
2. Plug these coordinates into the midpoint formula:
[tex]\[
M = \left( \frac{-6 + 9}{2}, \frac{-3 + (-7)}{2} \right)
\][/tex]
3. Calculate each part separately:
- The [tex]\(x\)[/tex]-coordinate of the midpoint:
[tex]\[
\frac{-6 + 9}{2} = \frac{3}{2} = 1.5
\][/tex]
- The [tex]\(y\)[/tex]-coordinate of the midpoint:
[tex]\[
\frac{-3 + (-7)}{2} = \frac{-10}{2} = -5
\][/tex]
4. Combine these values to find the coordinates of the midpoint:
[tex]\[
M = (1.5, -5)
\][/tex]
Therefore, the midpoint of the line segment with the given endpoints is [tex]\((1.5, -5)\)[/tex].
The correct answer is:
D. [tex]\((1.5, -5)\)[/tex]
