https://file.aiquickdraw.com/mathbot/file/1729646408180tod10399.jpg

The image shows a coordinate plane and a question asking for the result of a rotation. Specifically, it asks for the coordinates of point \( A' \), the image of point \( A(-1, -1) \), after a 90° rotation. 

Let's work through this step by step:

### Rotation of 90° Counterclockwise
When you rotate a point \( (x, y) \) 90° counterclockwise around the origin, the new coordinates \( (x', y') \) are:
\[
(x', y') = (-y, x)
\]
Thus, applying this rule to point \( A(-1, -1) \):
\[
A' = (-(-1), -1) = (1, -1)
\]

### Answer
The correct coordinates of \( A' \) after the 90° rotation are \( A'(1, -1) \).

Would you like further details on this topic or explanations on other transformations?

Here are 5 related questions you might find useful:
1. What is the formula for rotating a point 180°?
2. How do you rotate a point 270° counterclockwise?
3. How do you perform a reflection over the x-axis on a coordinate point?
4. What is the effect of translating a point by a vector \( (a, b) \)?
5. How do you find the center of rotation for two points?

**Tip**: When dealing with rotations, it is useful to visualize or sketch the rotation on a graph to avoid confusion.

Graph the preimage and image of each rotation. Determine the coordinates of A' after a 90° counterclockwise rotation for A(-1, -1).

Find the coordinates of point A' after a 90° counterclockwise rotation of point A(-1, -1). This geometry problem covers rotation transformations, using the formula (x', y') = (-y, x). Suitable for students in Grades 7-10.

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