To find the coordinates of the midpoint of the line segment [tex]\(\overline{KL}\)[/tex] with given endpoints [tex]\(K(-20, 3)\)[/tex] and [tex]\(L(12, -2)\)[/tex], we can use the midpoint formula. The midpoint formula states that if you have two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], 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]
Let's apply this formula step-by-step:
1. Identify the coordinates of the points [tex]\(K\)[/tex] and [tex]\(L\)[/tex]:
- [tex]\(K = (-20, 3)\)[/tex]
- [tex]\(L = (12, -2)\)[/tex]
2. Calculate the x-coordinate of the midpoint:
[tex]\[
x_{\text{mid}} = \frac{x_1 + x_2}{2} = \frac{-20 + 12}{2} = \frac{-8}{2} = -4
\][/tex]
3. Calculate the y-coordinate of the midpoint:
[tex]\[
y_{\text{mid}} = \frac{y_1 + y_2}{2} = \frac{3 + (-2)}{2} = \frac{1}{2} = 0.5
\][/tex]
Combining these results, the coordinates of the midpoint are:
[tex]\[
M = \left( -4, 0.5 \right)
\][/tex]
Thus, the coordinates of the midpoint of [tex]\(\overline{KL}\)[/tex] is:
[tex]\[
\left( -4, 0.5 \right)
\][/tex]
Among the given options, the coordinates [tex]\(\left(-4, \frac{1}{2} \right)\)[/tex] match our result.
