To find the midpoint of a line segment with given endpoints, we use the midpoint formula. The midpoint [tex]\(M\)[/tex] of a line segment with endpoints [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 endpoints [tex]\((1, -6)\)[/tex] and [tex]\((-3, 4)\)[/tex], we can find the midpoint as follows:
1. Calculate the x-coordinate of the midpoint:
[tex]\[
\text{midpoint}_x = \frac{1 + (-3)}{2} = \frac{1 - 3}{2} = \frac{-2}{2} = -1
\][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[
\text{midpoint}_y = \frac{-6 + 4}{2} = \frac{-6 + 4}{2} = \frac{-2}{2} = -1
\][/tex]
So, the coordinates of the midpoint are [tex]\((-1, -1)\)[/tex].
Thus, the midpoint of the line segment with endpoints [tex]\((1, -6)\)[/tex] and [tex]\((-3, 4)\)[/tex] is [tex]\(\boxed{(-1, -1)}\)[/tex].
