To find the coordinates of the midpoint [tex]\(N \)[/tex] of points [tex]\(K\)[/tex] and [tex]\(L\)[/tex], we will use the midpoint formula. The midpoint formula for two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] in a coordinate plane is given by:
[tex]\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Given the coordinates of point [tex]\(K\)[/tex] as [tex]\((-7, -6)\)[/tex] and point [tex]\(L\)[/tex] as [tex]\((1, 10)\)[/tex], let us apply the midpoint formula step-by-step.
1. Calculate the x-coordinate of the midpoint:
[tex]\[
x_{\text{mid}} = \frac{x_1 + x_2}{2} = \frac{-7 + 1}{2} = \frac{-6}{2} = -3
\][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[
y_{\text{mid}} = \frac{y_1 + y_2}{2} = \frac{-6 + 10}{2} = \frac{4}{2} = 2
\][/tex]
Therefore, the coordinates of point [tex]\( N \)[/tex] are [tex]\( (-3, 2) \)[/tex].
So, the correct answer is:
[tex]\[
\boxed{(-3, 2)}
\][/tex]
