Find the midpoint of the line segment joined the two points (2,3) and (4,1).

Answer

To find the midpoint of the line segment joining the points (2, 3) and (4, 1), we can use the midpoint formula. The midpoint \( M \) of a line segment with endpoints \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is given by:

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

### Step-by-Step Solution:

1. **Identify the coordinates of the points:**
- Let point A be \( (x_1, y_1) = (2, 3) \)
- Let point B be \( (x_2, y_2) = (4, 1) \)

2. **Substitute the coordinates into the midpoint formula:**
- The x-coordinate of the midpoint \( M \) is calculated as:
\[ x_M = \frac{x_1 + x_2}{2} = \frac{2 + 4}{2} \]
- The y-coordinate of the midpoint \( M \) is calculated as:
\[ y_M = \frac{y_1 + y_2}{2} = \frac{3 + 1}{2} \]

3. **Calculate the x-coordinate:**
- Add the x-coordinates:
\[ 2 + 4 = 6 \]
- Divide by 2:
\[ x_M = \frac{6}{2} = 3 \]

4. **Calculate the y-coordinate:**
- Add the y-coordinates:
\[ 3 + 1 = 4 \]
- Divide by 2:
\[ y_M = \frac{4}{2} = 2 \]

5. **Combine the results to find the midpoint:**
- Thus, the midpoint \( M \) is:
\[ M = (x_M, y_M) = (3, 2) \]

### Final Answer:
The midpoint of the line segment joining the points (2, 3) and (4, 1) is \( (3, 2) \).