To find the midpoint \( R \) of segment \( AM \), we use the midpoint formula:
\[ R = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
where \( (x_1, y_1) \) are the coordinates of point \( A\) and \( (x_2, y_2) \) are the coordinates of point \( M\).
Given:
- Point \( A = (-2, 4) \) where \( x_1 = -2 \) and \( y_1 = 4 \)
- Point \( M = (-2, 1) \) where \( x_2 = -2 \) and \( y_2 = 1 \)
Now, substitute these values into the midpoint formula:
- Calculate the x-coordinate of \( R \):
\[ x_R = \frac{-2 + -2}{2} = \frac{-4}{2} = -2 \]
- Calculate the y-coordinate of \( R \):
\[ y_R = \frac{4 + 1}{2} = \frac{5}{2} = 2.5 \]
Thus, the midpoint \( R \) is located at \( (-2, 2.5) \).
The correct answer is:
B. R is located at (-2, 2.5).