To rotate a point \((x, y)\) counterclockwise about the origin by \(270\) degrees, you can use the rotation formula. The general formula for rotating a point \((x, y)\) counterclockwise by an angle \(\theta\) is given by:
\[ (x', y') = (x \cos \theta - y \sin \theta, x \sin \theta + y \cos \theta) \]
For a rotation of \(270\) degrees, we convert this angle to radians:
\[ 270 \text{ degrees} = \frac{270 \pi}{180} = \frac{3\pi}{2} \text{ radians} \]
Next, we evaluate \(\cos(270^\circ)\) and \(\sin(270^\circ)\):
- \(\cos(270^\circ) = 0\)
- \(\sin(270^\circ) = -1\)
Substituting these values into the rotation formula:
\[ (x', y') = (x \cdot 0 - y \cdot (-1), x \cdot (-1) + y \cdot 0) \]
This simplifies to:
\[ (x', y') = (y, -x) \]
So, the new point after rotating the point \((x, y)\) counterclockwise by \(270\) degrees about the origin is:
\[ (y, -x) \]
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