To find the coordinates of the point Y' after a 180-degree counterclockwise rotation about the origin, we can use the formula for rotation. When a point (x, y) is rotated 180 degrees counterclockwise about the origin, it transforms according to the formula:
\[ (x, y) \to (-x, -y) \]
For the point Y given as Y(-2, 6), we apply the rotation:
- Negate the x-coordinate: -(-2) = 2
- Negate the y-coordinate: -(6) = -6
Thus, the coordinates of Y' after the 180-degree rotation about the origin are:
\[ Y'(2, -6) \]
So, the coordinates for Y' are \( (2, -6) \).