Question

what transformation is always the same as rotating a figure 180 degrees about the origin? 1 point reflecting over the line y = x rotating 90 degrees and then 180 degrees translating left 4 units and down 4 units reflecting over the origin

Explanation:

A 180-degree rotation about the origin maps a point $(x,y)$ to $(-x,-y)$. Reflecting a point over the origin also maps $(x,y)$ to $(-x,-y)$. The other options produce different coordinate mappings: reflecting over $y=x$ swaps $x$ and $y$, combining rotations gives a net 270-degree rotation, and translation shifts coordinates without sign changes.

Answer:

reflecting over the origin