What is a reflection over the origin equivalent to?

A reflection over the origin is equivalent to performing a 180-degree rotation around the origin. When you reflect a point across the origin, you effectively negate both its x and y coordinates, which results in a rotation that places the point in the opposite quadrant of the coordinate plane. This transformation corresponds to a half-turn, where each point moves to a position that is directly opposite its starting location, aligning with what happens in a 180-degree rotation.

This relationship can be visualized easily: for a point located at (x, y), reflecting over the origin transforms it to (-x, -y). If you were to rotate the point (x, y) by 180 degrees, it would also land at (-x, -y). Thus, the equivalence of reflection over the origin and a 180-degree rotation is established by both operations yielding the same result in the placement of a point in the coordinate plane.