To rotate a point \((x, y)\) clockwise about the origin by 270 degrees, we can use the following transformation.
Rotations in the coordinate system can be handled by using rotation matrices, but for specific angles like 90, 180, and 270 degrees, we can use simpler transformations.
A clockwise rotation by 270 degrees is equivalent to a counterclockwise rotation by 90 degrees. Therefore, we can find the new coordinates using the counterclockwise rotation transformation.
The transformation for a 90-degree counterclockwise rotation is: \[ (x', y') = (-y, x) \]
Thus, for a point \((x, y)\), performing a clockwise rotation of 270 degrees results in the new point: \[ (x', y') = (-y, x) \]
So, if you have a point \((x, y)\), the new point after a 270-degree clockwise rotation about the origin is: \[ (-y, x) \]
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