Infer the unique motion from this allowed family: translations, reflections across the \(x\text{-}\text{axis}\) or \(y\text{-}\text{axis}\), and \(90°/180°/270°\) rotations about the origin. It maps segment \(AB\) to \(CD\) with \(A(0,0)\to~C(2,3)\) and \(B(4,0)\to~D(6,3)\).

A segment mapping must send both labeled endpoints correctly, not merely place one endpoint. Compute the displacement from each source endpoint to its assigned image and compare the two vectors; a common vector identifies one rule, while any competing reflection or rotation must pass both endpoint checks as well.