The point A(1, 2) is rotated 270 degrees about the origin. (Counterclockwise)

To rotate a point \((x, y)\) counterclockwise by \(270^\circ\) about the origin, you can use the following transformation:

\[
(x, y) \rightarrow (y, -x)
\]

For the point \(A(1, 2)\):

1. Identify the coordinates: \(x = 1\), \(y = 2\).
2. Apply the rotation transformation:

\[
A' = (y, -x) = (2, -1)
\]

Thus, the ordered pair for \(A'\) after a \(270^\circ\) counterclockwise rotation about the origin is \(\boxed{(2, -1)}\).