Let's find the coordinates of point M and point N step-by-step.
1. Coordinates of Points K and L:
- Point [tex]\( K \)[/tex] has coordinates (-7, -6).
- Point [tex]\( L \)[/tex] has coordinates (1, 10).
2. Finding the Midpoint M:
The midpoint [tex]\( M \)[/tex] of two points [tex]\( K(x_1, y_1) \)[/tex] and [tex]\( L(x_2, y_2) \)[/tex] can be found using the midpoint formula:
[tex]\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Substituting the coordinates of [tex]\( K \)[/tex] and [tex]\( L \)[/tex]:
[tex]\[
M_x = \frac{-7 + 1}{2} = \frac{-6}{2} = -3
\][/tex]
[tex]\[
M_y = \frac{-6 + 10}{2} = \frac{4}{2} = 2
\][/tex]
Therefore, the coordinates of point [tex]\( M \)[/tex] are:
[tex]\[
M = (-3, 2)
\][/tex]
3. Finding the Midpoint N:
The midpoint [tex]\( N \)[/tex] of two points [tex]\( M(x_1, y_1) \)[/tex] and [tex]\( L(x_2, y_2) \)[/tex] can be found using the midpoint formula again:
[tex]\[
N = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Using the coordinates of [tex]\( M \)[/tex] and [tex]\( L \)[/tex]:
[tex]\[
N_x = \frac{-3 + 1}{2} = \frac{-2}{2} = -1
\][/tex]
[tex]\[
N_y = \frac{2 + 10}{2} = \frac{12}{2} = 6
\][/tex]
Therefore, the coordinates of point [tex]\( N \)[/tex] are:
[tex]\[
N = (-1, 6)
\][/tex]
So, the correct answer is:
A. [tex]\((-1, 6)\)[/tex]
