P and Q have co-ordinates (0, 5) and (-2, 4).
P is invariant when reflected in an axis. Name the axis.

Answer

To solve the problem, we need to determine which axis the point P (0, 5) remains unchanged when reflected across it.

### Step-by-step Solution:

1. **Identify the Coordinates of Point P**:
- The coordinates of point P are given as (0, 5).

2. **Understand Invariance**:
- A point is said to be invariant when it does not change its position after being reflected across a certain axis.

3. **Consider Reflection Across the Y-Axis**:
- When reflecting a point across the y-axis, the x-coordinate changes sign while the y-coordinate remains the same.
- For point P (0, 5), reflecting it across the y-axis:
- New coordinates = (-x, y) = (-0, 5) = (0, 5).
- Since the coordinates remain (0, 5), point P is invariant when reflected across the y-axis.

4. **Consider Reflection Across the X-Axis**:
- When reflecting a point across the x-axis, the y-coordinate changes sign while the x-coordinate remains the same.
- For point P (0, 5), reflecting it across the x-axis:
- New coordinates = (x, -y) = (0, -5).
- The coordinates change to (0, -5), so point P is not invariant when reflected across the x-axis.

5. **Conclusion**:
- Since point P (0, 5) remains unchanged only when reflected across the y-axis, we conclude that the required axis is the y-axis.

### Final Answer:
The axis across which point P is invariant is the **y-axis**.

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