To find the point \( P' \) resulting from a 270-degree counterclockwise rotation of a point \( P(x, y) \) about the origin, we can use the following transformation formulas:
A 270-degree counterclockwise rotation about the origin can be accomplished by applying the rotation transformation: \[ P'(x', y') = (y, -x) \]
This means:
- The x-coordinate of the point after rotation becomes the y-coordinate of the original point.
- The y-coordinate of the point after rotation becomes the negative of the x-coordinate of the original point.
If we apply this transformation:
- Start with point \( P(x, y) \).
- After the rotation, the new coordinates will be \( P'(y, -x) \).
For example, if we have a point \( P(2, 3) \):
- After a 270-degree counterclockwise rotation, the new point \( P' \) will be \( (3, -2) \).
So, if you have a specific point \( P \) (you can substitute its coordinates into the above transformation), you will get the corresponding point \( P' \) after the rotation. If you don't have specific coordinates for \( P \), the general result is: \[ P' = (y, -x) \]