What is mid - point of line segment AB, where A (-5,0) and B(0,5) ?

Answer

To find the midpoint of the line segment AB where A is (-5, 0) and B is (0, 5), we can use the midpoint formula. The formula for the midpoint M of a line segment with endpoints A (x1, y1) and B (x2, y2) is given by:

\[ M = \left( \frac{x1 + x2}{2}, \frac{y1 + y2}{2} \right) \]

### Step-by-Step Solution:

1. **Identify the coordinates of points A and B**:
- Point A has coordinates \( A(-5, 0) \) which means \( x1 = -5 \) and \( y1 = 0 \).
- Point B has coordinates \( B(0, 5) \) which means \( x2 = 0 \) and \( y2 = 5 \).

2. **Substitute the coordinates into the midpoint formula**:
- Using the formula:
\[ M = \left( \frac{x1 + x2}{2}, \frac{y1 + y2}{2} \right) \]
- Substitute the values:
\[ M = \left( \frac{-5 + 0}{2}, \frac{0 + 5}{2} \right) \]

3. **Calculate the x-coordinate of the midpoint**:
- Calculate \( \frac{-5 + 0}{2} \):
\[ \frac{-5}{2} = -\frac{5}{2} \]

4. **Calculate the y-coordinate of the midpoint**:
- Calculate \( \frac{0 + 5}{2} \):
\[ \frac{5}{2} = \frac{5}{2} \]

5. **Combine the results to find the midpoint**:
- The midpoint M is:
\[ M = \left(-\frac{5}{2}, \frac{5}{2}\right) \]

### Final Answer:
The midpoint of the line segment AB is \( M\left(-\frac{5}{2}, \frac{5}{2}\right) \).

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