Find the midpoint of the line joining the points `(7, 6) and (-3, -4)`.

Answer

To find the midpoint of the line segment joining the points \( (7, 6) \) and \( (-3, -4) \), we can use the midpoint formula. The midpoint \( M \) of a line segment joining two points \( A(x_1, y_1) \) 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 \( A = (x_1, y_1) = (7, 6) \)
- Let \( B = (x_2, y_2) = (-3, -4) \)

2. **Substitute the coordinates into the midpoint formula**:
- For the x-coordinate of the midpoint:
\[ x_M = \frac{x_1 + x_2}{2} = \frac{7 + (-3)}{2} \]
- For the y-coordinate of the midpoint:
\[ y_M = \frac{y_1 + y_2}{2} = \frac{6 + (-4)}{2} \]

3. **Calculate the x-coordinate**:
- Simplifying the x-coordinate:
\[ x_M = \frac{7 - 3}{2} = \frac{4}{2} = 2 \]

4. **Calculate the y-coordinate**:
- Simplifying the y-coordinate:
\[ y_M = \frac{6 - 4}{2} = \frac{2}{2} = 1 \]

5. **Combine the results to find the midpoint**:
- Therefore, the midpoint \( M \) is:
\[ M = (x_M, y_M) = (2, 1) \]

### Final Answer:
The midpoint of the line joining the points \( (7, 6) \) and \( (-3, -4) \) is \( (2, 1) \).

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