Question

Identify the point that applies a rotation function mapping for P in a 270-degree counterclockwise rotation about the origin.

A 270-degree counterclockwise rotation about the origin will plot P' at point __.

Answer 1

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:
1. Start with point \( P(x, y) \).
2. 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:
\[
P' = (y, -x)
\]