To determine the coordinates of the midpoint of the line segment [tex]\(\overline{EF}\)[/tex] with points [tex]\(E(-12, 5)\)[/tex] and [tex]\(F(7, -9)\)[/tex], we will use the midpoint formula. The midpoint [tex]\(M\)[/tex] of a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Given the points [tex]\(E(-12, 5)\)[/tex] and [tex]\(F(7, -9)\)[/tex]:
1. Identify the coordinates of point [tex]\(E\)[/tex]: [tex]\(E = (-12, 5)\)[/tex].
2. Identify the coordinates of point [tex]\(F\)[/tex]: [tex]\(F = (7, -9)\)[/tex].
Next, apply the midpoint formula:
[tex]\[
\text{Midpoint } M = \left( \frac{-12 + 7}{2}, \frac{5 + (-9)}{2} \right)
\][/tex]
Now, proceed step-by-step to find the coordinates:
1. Calculate the [tex]\(x\)[/tex]-coordinate of the midpoint:
[tex]\[
\frac{-12 + 7}{2} = \frac{-5}{2} = -\frac{5}{2}
\][/tex]
2. Calculate the [tex]\(y\)[/tex]-coordinate of the midpoint:
[tex]\[
\frac{5 + (-9)}{2} = \frac{-4}{2} = -2
\][/tex]
Therefore, the coordinates of the midpoint [tex]\(M\)[/tex] are:
[tex]\[
M = \left( -\frac{5}{2}, -2 \right)
\][/tex]
The correct answer is [tex]\(\left( -\frac{5}{2}, -2 \right)\)[/tex].
