To find the midpoint [tex]\( M \)[/tex] of a line segment with endpoints [tex]\( A(-6,4) \)[/tex] and [tex]\( B(4,2) \)[/tex], we use the midpoint formula. The midpoint formula states that the coordinates of the midpoint [tex]\( M \)[/tex] are given by:
[tex]\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Here, the coordinates of point [tex]\( A \)[/tex] are [tex]\( (x_1, y_1) = (-6, 4) \)[/tex], and the coordinates of point [tex]\( B \)[/tex] are [tex]\( (x_2, y_2) = (4, 2) \)[/tex].
Step-by-step, we perform the following calculations:
1. Calculate the x-coordinate of the midpoint:
[tex]\[
x_{\text{mid}} = \frac{x_1 + x_2}{2} = \frac{-6 + 4}{2}
\][/tex]
Simplify the numerator:
[tex]\[
-6 + 4 = -2
\][/tex]
Thus:
[tex]\[
x_{\text{mid}} = \frac{-2}{2} = -1
\][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[
y_{\text{mid}} = \frac{y_1 + y_2}{2} = \frac{4 + 2}{2}
\][/tex]
Simplify the numerator:
[tex]\[
4 + 2 = 6
\][/tex]
Thus:
[tex]\[
y_{\text{mid}} = \frac{6}{2} = 3
\][/tex]
Therefore, the coordinates of the midpoint [tex]\( M \)[/tex] are [tex]\((-1, 3)\)[/tex].
So, the midpoint [tex]\( M \)[/tex] of the segment with endpoints [tex]\( A(-6, 4) \)[/tex] and [tex]\( B(4, 2) \)[/tex] is
[tex]\[
M(-1.0, 3.0).
\][/tex]
