To find the midpoint of a line segment with endpoints [tex]\( R(x_1, y_1) \)[/tex] and [tex]\( T(x_2, y_2) \)[/tex], we use the midpoint formula. The midpoint [tex]\( M \)[/tex] is given by the formula:
[tex]\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
For the given endpoints [tex]\( R(-3, 4) \)[/tex] and [tex]\( T(-7, -3) \)[/tex], we need to plug these coordinates into the midpoint formula.
1. First, calculate the x-coordinate of the midpoint:
[tex]\[
\frac{x_1 + x_2}{2} = \frac{-3 + (-7)}{2}
\][/tex]
Simplify the expression inside the parentheses:
[tex]\[
\frac{-3 - 7}{2} = \frac{-10}{2} = -5
\][/tex]
2. Next, calculate the y-coordinate of the midpoint:
[tex]\[
\frac{y_1 + y_2}{2} = \frac{4 + (-3)}{2}
\][/tex]
Simplify the expression inside the parentheses:
[tex]\[
\frac{4 - 3}{2} = \frac{1}{2} = 0.5
\][/tex]
So, the coordinates of the midpoint are:
[tex]\[
\left( -5, 0.5 \right)
\][/tex]
Therefore, the correct answer is:
[tex]\[
\left(-5, \frac{1}{2}\right)
\][/tex]
