What is the transformation for a reflection across the X-axis?

When reflecting a point across the X-axis in the coordinate plane, the Y-coordinate of the point changes sign while the X-coordinate remains the same. This can be mathematically expressed as taking a point ((x, y)) and transforming it to ((x, -y)).

This transformation works as follows:

1. If you have a point above the X-axis (where (y) is positive), the reflection will move it to the same distance below the X-axis, resulting in a negative Y-coordinate.
2. Conversely, if the point is initially below the X-axis (where (y) is negative), reflecting it across the X-axis will move it to the same distance above the X-axis, making the Y-coordinate positive.

In this case, since the transformation ((x, y) = (x, -y)) accurately represents the required change when performing a reflection across the X-axis, this confirms its correctness for this operation.

The other options represent different transformations that do not match the effect of reflecting over the X-axis. For instance, keeping both coordinates the same, switching coordinates, or negative inversions are not consistent with the reflection process described.