What is the y coordinate of the mid-point of A(-1, 3) and B(1, -1)?

Options

A. 1
B. 2
C. 3
D. 4

Answer

To find the y-coordinate of the midpoint of points A(-1, 3) and B(1, -1), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Coordinates**:
- Point A has coordinates \( A(-1, 3) \).
- Point B has coordinates \( B(1, -1) \).

2. **Use the Midpoint Formula**:
The formula for the midpoint \( M \) of two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

3. **Substitute the Coordinates into the Formula**:
- Here, \( x_1 = -1 \), \( y_1 = 3 \), \( x_2 = 1 \), and \( y_2 = -1 \).
- Substitute these values into the midpoint formula:
\[ M = \left( \frac{-1 + 1}{2}, \frac{3 + (-1)}{2} \right) \]

4. **Calculate the x-coordinate**:
- The x-coordinate is:
\[ \frac{-1 + 1}{2} = \frac{0}{2} = 0 \]

5. **Calculate the y-coordinate**:
- The y-coordinate is:
\[ \frac{3 + (-1)}{2} = \frac{3 - 1}{2} = \frac{2}{2} = 1 \]

6. **Conclusion**:
- The y-coordinate of the midpoint \( M \) is \( 1 \).

### Final Answer:
The y-coordinate of the midpoint of A(-1, 3) and B(1, -1) is **1**.