To find the coordinates of the point W' after a 90-degree counterclockwise rotation about the origin, we can use the rotation mapping rule for 90 degrees, which states:
\[ (x, y) \rightarrow (-y, x) \]
Given the coordinates of point W as (-4, 7), we can apply the rotation rule:
- Take the y-coordinate (7) and make it the new x-coordinate.
- Take the x-coordinate (-4) and make it the new y-coordinate, but negate it.
So:
- The original coordinates of W are (-4, 7).
- After applying the rotation:
- New x-coordinate: -y = -7
- New y-coordinate: x = -4
Thus, the coordinates of W' after a 90-degree rotation about the origin are:
\[ W' = (-7, -4) \]
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