To find the coordinates of the point \( W' \) after a 90-degree counterclockwise rotation about the origin, you can use the rotation mapping rule for a 90-degree counterclockwise rotation. The rule is:
\[ (x, y) \to (-y, x) \]
Given the coordinates of point \( W \) as \( (-3, 7) \):
- Take the \( x \) coordinate: \( -3 \)
- Take the \( y \) coordinate: \( 7 \)
Applying the rotation rule:
\[ W' = (-y, x) = (-7, -3) \]
Thus, the coordinates of \( W' \) after the rotation are \( W'(-7, -3) \).