The mirror image of the point (1, 2, 3) in a plane is (-1,2,-3) . Which of the following points lies on this plane?

Options

A. (0, 1, 2)
B. (0, 2, 0)
C. (0, 2, 1)
D. (1, -1, 1)

Explanation

To solve the problem, we need to find the point that lies on the plane which is the perpendicular bisector of the segment joining the point \( A(1, 2, 3) \) and its mirror image \( B(-1, 2, -3) \).

### Step-by-Step Solution:

1. **Identify the Points**:
- Let point \( A \) be \( (1, 2, 3) \).
- Let point \( B \) be \( (-1, 2, -3) \).

2. **Calculate the Midpoint**:
The midpoint \( M \) of the segment joining points \( A \) and \( B \) can be calculated using the midpoint formula:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2} \right) \]
Substituting the coordinates of points \( A \) and \( B \):
\[ M = \left( \frac{1 + (-1)}{2}, \frac{2 + 2}{2}, \frac{3 + (-3)}{2} \right) = \left( \frac{0}{2}, \frac{4}{2}, \frac{0}{2} \right) = (0, 2, 0) \]

3. **Conclusion**:
The midpoint \( M(0, 2, 0) \) lies on the plane of reflection. Therefore, this point is the one that lies on the plane.

### Final Answer:
The point that lies on the plane is \( (0, 2, 0) \).