Question

A(-2, 1) imagine a 270(counterclockwise) rotation, what would A' be?

Answer 1

To perform a 270-degree counterclockwise rotation around the origin on the point \( A(-2, 1) \), we can use the following transformation rules for coordinates:

1. A 90-degree counterclockwise rotation transforms a point \( (x, y) \) to \( (-y, x) \).
2. A 180-degree counterclockwise rotation transforms \( (x, y) \) to \( (-x, -y) \).
3. A 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation. Therefore, we can use the 90-degree clockwise transformation:

- \( (x, y) \) to \( (y, -x) \).

Applying this to the point \( A(-2, 1) \):

- \( x = -2 \)
- \( y = 1 \)

After the transformation, we get:

\[
A' = (y, -x) = (1, -(-2)) = (1, 2)
\]

So the coordinates of \( A' \) after a 270-degree counterclockwise rotation are \( A'(1, 2) \).