To find the midpoint of a line segment with given endpoints, we use the midpoint formula. The formula to find the midpoint [tex]\(M\)[/tex] between two points [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 points [tex]\((-6, 8)\)[/tex] and [tex]\((-4, -14)\)[/tex], we can substitute these values into the midpoint formula.
So, let's substitute the values:
1. For the [tex]\(x\)[/tex]-coordinate:
[tex]\[ x = \frac{-6 + (-4)}{2} = \frac{-6 - 4}{2} = \frac{-10}{2} = -5.0 \][/tex]
2. For the [tex]\(y\)[/tex]-coordinate:
[tex]\[ y = \frac{8 + (-14)}{2} = \frac{8 - 14}{2} = \frac{-6}{2} = -3.0 \][/tex]
Thus, the midpoint of the segment with the given endpoints [tex]\((-6, 8)\)[/tex] and [tex]\((-4, -14)\)[/tex] is:
[tex]\[
\boxed{(-5.0, -3.0)}
\][/tex]
