To determine the midpoint of a line segment given its endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], you can use the midpoint formula. The midpoint [tex]\(M\)[/tex] is calculated using the following formula:
[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]:
1. First, find the x-coordinate of the midpoint:
[tex]\[
x_{\text{mid}} = \frac{x_1 + x_2}{2} = \frac{1 + (-3)}{2} = \frac{1 - 3}{2} = \frac{-2}{2} = -1
\][/tex]
2. Next, find the y-coordinate of the midpoint:
[tex]\[
y_{\text{mid}} = \frac{y_1 + y_2}{2} = \frac{-6 + 4}{2} = \frac{-6 + 4}{2} = \frac{-2}{2} = -1
\][/tex]
Therefore, the midpoint of the line segment is [tex]\((-1, -1)\)[/tex].
Given the provided options, the correct answer is:
A. [tex]\((-1, -1)\)[/tex]
