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If R is the midpoint of segment AM¯¯¯¯¯¯¯¯¯ , find midpoint R .(1 point)ResponsesR is located at (−2,2.5).upper B is located at left parenthesis negative 2 comma 2.5 right parenthesis .R is located at (0,2.5).upper B is located at left parenthesis 0 comma 2.5 right parenthesis .R is located at (−2,−2).upper B is located at left parenthesis negative 2 comma negative 2 right parenthesis .R is located at (−2,7).

To solve for the midpoint \( R \) of segment \( \overline{AM} \), we will use the midpoint formula. The formula for the midpoint of a segment with endpoints \( A(x_1, y_1) \) and \( M(x_2, y_2) \) is given by:

\[
R\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

From the image:
- Point \( A \) is \( (-2, 4) \)
- Point \( M \) is \( (-2, 1) \)

### Step 1: Apply the midpoint formula

\[
x_R = \frac{-2 + (-2)}{2} = \frac{-4}{2} = -2
\]
\[
y_R = \frac{4 + 1}{2} = \frac{5}{2} = 2.5
\]

### Result
The midpoint \( R \) is located at \( (-2, 2.5) \).

Let me know if you would like further explanation or more details!

Here are 5 related questions for further practice:
1. How do you find the midpoint if the coordinates of two points are given as decimals?
2. What is the significance of the midpoint in geometry?
3. If \( R \) is the midpoint of a horizontal line segment, how does the y-coordinate of \( R \) relate to the endpoints?
4. How would the formula for the midpoint change if you were working in 3D space?
5. Can the midpoint formula be used to check if three points are collinear?

**Tip:** Always remember to calculate both the x and y components separately when using the midpoint formula!

If R is the midpoint of segment AM, find midpoint R.

Learn how to find the midpoint of segment AM using the midpoint formula, given points A (-2, 4) and M (-2, 1). This problem explores essential concepts of coordinate geometry, including applying the midpoint formula. Suitable for Grades 7-9 students.

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