Question

If R is the midpoint of segment AM, find midpoint R.
Point A: (-2, 4)
Point M: (-2, 1)

A. R is located at (-2, -2)
B. R is located at (-2, 2.5)
C. R is located at (-2, 7)
D. R is located at (0, 2.5)

Answer 1

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:

1. Calculate the x-coordinate of \( R \):

\[
x_R = \frac{-2 + -2}{2} = \frac{-4}{2} = -2
\]

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)**.