https://file.aiquickdraw.com/mathbot/file/17294405138109lqzkysl.jpg

The image shows a rotation problem asking to determine the coordinates of point \( A' \) after a 90-degree rotation of point \( A(2, 1) \).

To rotate a point 90 degrees counterclockwise around the origin, the transformation rule is:
\[
(x, y) \to (-y, x)
\]

Applying this rule to \( A(2, 1) \):
\[
A(2, 1) \to A'(-1, 2)
\]

So, the coordinates of \( A' \) after a 90-degree rotation are \( A'(-1, 2) \).

Thus, the correct answer is:
**A'(-1, -2)**.

Would you like further explanation or details?

### Related Questions:
1. How would the coordinates of \( A(2, 1) \) change for a 180-degree rotation?
2. What is the transformation rule for a 270-degree counterclockwise rotation?
3. How would you perform a reflection over the x-axis for the point \( A(2, 1) \)?
4. What is the formula for rotating a point clockwise by 90 degrees?
5. How does a dilation from the origin affect the coordinates of a point?

### Tip:
Remember that rotations are counterclockwise by default unless otherwise specified!

Graph the preimage and image of each rotation. Determine the coordinates of A'.

Learn how to find the coordinates of a point after a 90-degree counterclockwise rotation around the origin. This problem involves understanding rotation transformations in a coordinate plane, using the rule (x, y) → (-y, x). Suitable for students in Grades 7-9.

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