To find the midpoint of a line segment with given endpoints, we use the midpoint formula. The midpoint [tex]\((M)\)[/tex] of a segment connecting 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]
Here, the endpoints are [tex]\((1, -6)\)[/tex] and [tex]\((-3, 4)\)[/tex]. Let's substitute these coordinates into the formula step by step.
1. Finding the x-coordinate of the midpoint:
[tex]\[
\text{midpoint}_x = \frac{x_1 + x_2}{2} = \frac{1 + (-3)}{2} = \frac{1 - 3}{2} = \frac{-2}{2} = -1
\][/tex]
2. Finding the y-coordinate of the midpoint:
[tex]\[
\text{midpoint}_y = \frac{y_1 + y_2}{2} = \frac{-6 + 4}{2} = \frac{-6 + 4}{2} = \frac{-2}{2} = -1
\][/tex]
So, the midpoint of the line segment with endpoints [tex]\((1, -6)\)[/tex] and [tex]\((-3, 4)\)[/tex] is [tex]\((-1, -1)\)[/tex].
From the given choices:
A. [tex]\((-2, -2)\)[/tex]
B. [tex]\((-1, -1)\)[/tex]
C. [tex]\((-2, -1)\)[/tex]
D. [tex]\((-1, -2)\)[/tex]
The correct answer is [tex]\( \boxed{(-1, -1)} \)[/tex].
