To find the midpoint [tex]\( M \)[/tex] of a segment with given endpoints [tex]\( L(-6, 17) \)[/tex] and [tex]\( N(-7, 12) \)[/tex], we use the midpoint formula. The midpoint formula for a segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Here, the coordinates of the endpoints are:
[tex]\[
L(x_1, y_1) = (-6, 17)
\][/tex]
[tex]\[
N(x_2, y_2) = (-7, 12)
\][/tex]
Plugging in these values into the midpoint formula, we get:
[tex]\[
M_x = \frac{-6 + (-7)}{2}
\][/tex]
[tex]\[
M_x = \frac{-6 - 7}{2}
\][/tex]
[tex]\[
M_x = \frac{-13}{2}
\][/tex]
[tex]\[
M_x = -6.5
\][/tex]
Similarly for the [tex]\( y \)[/tex]-coordinate:
[tex]\[
M_y = \frac{17 + 12}{2}
\][/tex]
[tex]\[
M_y = \frac{29}{2}
\][/tex]
[tex]\[
M_y = 14.5
\][/tex]
Therefore, the midpoint [tex]\( M \)[/tex] of the segment with endpoints [tex]\( L(-6, 17) \)[/tex] and [tex]\( N(-7, 12) \)[/tex] is:
[tex]\[
M = (-6.5, 14.5)
\][/tex]
So, the correct coordinates are [tex]\((-6.5, 14.5)\)[/tex].
