To rotate a point \((x, y)\) clockwise about the origin by 180 degrees, you can use the rotation transformation formula:
\[ (x, y) \rightarrow (-x, -y) \]
For the point \((1, 2)\):
\[ (1, 2) \rightarrow (-1, -2) \]
Thus, the new point after a 180-degree clockwise rotation about the origin is \((-1, -2)\).