In geometry, how is a reflection over the x-axis performed?

To perform a reflection over the x-axis in geometry, you only change the sign of the y-coordinate of a point while keeping the x-coordinate unchanged. This means that if you have a point with coordinates (x, y), after reflecting it over the x-axis, the new coordinates will be (x, -y).

This geometric transformation is based on the property that reflecting a point across a horizontal line (which the x-axis is) alters vertical distance while preserving horizontal placement. It is important to note that the x-coordinate remains constant in this transformation, so any other method such as switching coordinates or rotating does not describe the reflection process accurately.