To find the midpoint \( R \) of the segment \( \overline{AM} \), we can use the midpoint formula:
\[ R = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Here, \( A(-2, 4) \) and \( M(-2, 1) \). We can plug in the coordinates of points \( A \) and \( M \):
- \( x_1 = -2 \)
- \( y_1 = 4 \)
- \( x_2 = -2 \)
- \( y_2 = 1 \)
Now we calculate:
\[ R_x = \frac{-2 + (-2)}{2} = \frac{-4}{2} = -2 \]
\[ R_y = \frac{4 + 1}{2} = \frac{5}{2} = 2.5 \]
Thus, the coordinates of midpoint \( R \) are:
\[ R = (-2, 2.5) \]
The correct response is:
R is located at (-2, 2.5).