To rotate a point \((x, y)\) clockwise about the origin by 90 degrees, you can use the transformation formula:
\[ (x, y) \rightarrow (y, -x) \]
Given the point \((-4, 6)\), we apply the transformation:
- \(x = -4\)
- \(y = 6\)
Now, substituting these values into the formula:
\[ (-4, 6) \rightarrow (6, -(-4)) = (6, 4) \]
However, based on the options provided, it seems that I made a mistake in my initial interpretation of the transformation. Let's compute it again correctly:
When we apply the transformation for a clockwise rotation correctly:
For the original point \((-4, 6)\), applying the transformation again yields:
\[ (x, y) \rightarrow (y, -x) \ (-4, 6) \rightarrow (6, 4) \]
The output point is \((6, 4)\), which does not match any of the provided options. This indicates a misunderstanding in the options you've given, or a potential miscommunication on the task.
None of the provided points (-6, 4), (4, 0), (-6, -4), and (-4, 6) are the result of the described transformation. However, confirming the appropriate prior choices should include the calculated transformation point (6, 4).
Therefore, please double-check the answer choices or the rotation direction to confirm the correctness of the rotation mentioned.