To apply a 270-degree counterclockwise rotation about the origin, we can use the rotation transformation formulas. The formula for rotating a point \( (x, y) \) by 270 degrees counterclockwise is given by:
\[ (x', y') = (y, -x) \]
For point \( P \) which is at \( (4, 1) \):
\[ x = 4, \quad y = 1 \]
Applying the rotation:
\[ x' = y = 1 \] \[ y' = -x = -4 \]
Thus, the new coordinates after the rotation \( P' \) will be:
\[ P' = (1, -4) \]
Therefore, the point \( P' \) will be at point (1, -4).
The correct answer is Point 4: (1, -4).