To perform a counterclockwise rotation of a point around the origin, you can use the rotation formula. The formula for a 180° rotation about the origin is:
\[ (x, y) \rightarrow (-x, -y) \]
Given the point \( Y(-2, 6) \):
- Apply the rotation:
- \( x = -2 \) becomes \( -(-2) = 2 \)
- \( y = 6 \) becomes \( -(6) = -6 \)
Thus, the coordinates of the image of \( Y \) after a 180° counterclockwise rotation around the origin are:
\[ Y' = (2, -6) \]
Among the given options, the correct choice is:
\[ Y'(2, -6) \]