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Bot GPT 4-o mini To find the coordinates of a point after a 270-degree clockwise rotation about the origin, you can use the rotation transformation formulas.
The general transformation for rotating a point \((x, y)\) counterclockwise by an angle \(\theta\) (in this case, \(-270^{\circ}\) or \(90^{\circ}\) clockwise) is given by:
\[
(x', y') = (y, -x)
\]
So, if the point \(Y\) has coordinates \((x, y)\), after a 270-degree clockwise rotation, the new coordinates will be:
1. Swap \(x\) and \(y\).
2. Change the sign of the new \(x\).
Let's label the original coordinates of the point \(Y\) as \((x, y)\).
Assuming for this problem that the original coordinates \(Y\) are given somewhere in the context, you'll apply the transformation accordingly.
Based on the response options:
- \(Y′(1,9)\)
- \(Y′(−9,1)\)
- \(Y′(1,−9)\)
- \(Y′(−1,9)\)
If we consider a hypothetical original point \(Y(9, 1)\):
1. Swapping gives \((1, 9)\).
2. Changing the sign of the new x-coordinate gives \((-1, 9)\).
Thus the answer would be \(Y′(−1,9)\).
If you can provide the original coordinates of point Y, I can calculate the final answer more accurately.