Find the co -ordinates of the mid point of the join of the points A(3,5,7) and B(-3,-3,1)

Answer

To find the coordinates of the midpoint of the line segment joining the points A(3, 5, 7) and B(-3, -3, 1), we can use the midpoint formula for three-dimensional coordinates.

### Step-by-Step Solution:

1. **Identify the Coordinates of Points A and B**:
- Point A has coordinates \( A(3, 5, 7) \).
- Point B has coordinates \( B(-3, -3, 1) \).

2. **Use the Midpoint Formula**:
The midpoint \( M \) of the line segment joining two points \( A(x_1, y_1, z_1) \) and \( B(x_2, y_2, z_2) \) is given by the formula:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2} \right) \]

3. **Substitute the Coordinates into the Formula**:
- For the x-coordinate:
\[ x_M = \frac{x_1 + x_2}{2} = \frac{3 + (-3)}{2} = \frac{3 - 3}{2} = \frac{0}{2} = 0 \]
- For the y-coordinate:
\[ y_M = \frac{y_1 + y_2}{2} = \frac{5 + (-3)}{2} = \frac{5 - 3}{2} = \frac{2}{2} = 1 \]
- For the z-coordinate:
\[ z_M = \frac{z_1 + z_2}{2} = \frac{7 + 1}{2} = \frac{8}{2} = 4 \]

4. **Combine the Results**:
The coordinates of the midpoint \( M \) are:
\[ M(0, 1, 4) \]

### Final Answer:
The coordinates of the midpoint of the line segment joining points A and B are \( M(0, 1, 4) \).