To find the coordinates of A' after a counterclockwise rotation of 270° about the origin, you can use the rotation transformation formula.
A counterclockwise rotation of 270° is equivalent to a clockwise rotation of 90°. The transformation for rotating a point (x, y) 90° clockwise is given by:
\[ (x, y) \rightarrow (y, -x) \]
Now, let’s apply this transformation to each of the possible original points to see which one matches the options given.
Suppose A has coordinates (1, 2):
- Applying the transformation: \[ (1, 2) \rightarrow (2, -1) \]
Now, let's check each of the options given for A:
- (1, 2) → (2, -1) (Matches)
- (−1, −2) → (−2, 1) (Does not match)
- (1, 1) → (1, -1) (Does not match)
- (2, −1) → (−1, -2) (Does not match)
The correct choice for the coordinates of A' after a 270° counterclockwise rotation about the origin is:
\((2, -1)\).