To perform a 270-degree clockwise rotation about the origin on a point \((x, y)\), we can use the standard rotation transformation formulas. The transformation for a clockwise rotation can be expressed as follows:
\[ (x, y) \rightarrow (y, -x) \]
For the point \(Y (1, 9)\), we can apply the transformation:
- Original coordinates: \( (1, 9) \)
- Apply the rotation:
- New x-coordinate: \( y = 9 \)
- New y-coordinate: \( -x = -1 \)
So, after a 270-degree clockwise rotation, the new coordinates are:
\[ (9, -1) \]
However, your answer choices don't include \((9, -1)\). Let's check the possible answer choices:
- \( Y (1, -9) \)
- \( Y (-1, 9) \)
- \( Y (-9, 1) \)
Upon re-evaluation, it appears no option reflects the result, confirming we need the expected point from the rotation transformation. Based on the original point you provided, none of the answer choices match the transformation. It might be beneficial to verify in case there's any slight misrepresentation of details or numeric entries in the selected options.
Nevertheless, if your starting point was indeed (1,9), then the closest valid option isn't satisfied as illustrated. If the transformation was intended for another coordinate, revise accordingly. Feel free to check back in with those coordinates!
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