To find the coordinates of the midpoint of segment [tex]\(\overline{RT}\)[/tex] with endpoints [tex]\(R(1, 1)\)[/tex] and [tex]\(T(-7, -2)\)[/tex], we use the midpoint formula. The midpoint [tex]\(M\)[/tex] of a segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] can be found using the following formula:
[tex]\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Given the endpoints [tex]\(R(1, 1)\)[/tex] and [tex]\(T(-7, -2)\)[/tex]:
- [tex]\(x_1 = 1\)[/tex]
- [tex]\(y_1 = 1\)[/tex]
- [tex]\(x_2 = -7\)[/tex]
- [tex]\(y_2 = -2\)[/tex]
We substitute these values into the midpoint formula:
1. Calculate the x-coordinate of the midpoint:
[tex]\[
\frac{x_1 + x_2}{2} = \frac{1 + (-7)}{2} = \frac{1 - 7}{2} = \frac{-6}{2} = -3
\][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[
\frac{y_1 + y_2}{2} = \frac{1 + (-2)}{2} = \frac{1 - 2}{2} = \frac{-1}{2} = -0.5
\][/tex]
Thus, the coordinates of the midpoint [tex]\(M\)[/tex] are:
[tex]\[
\left( -3, -0.5 \right)
\][/tex]
Hence, the correct answer is:
[tex]\(\left(-3, -\frac{1}{2}\right)\)[/tex].
