To rotate a point \((x, y)\) counterclockwise about the origin by \(270\) degrees, you can use the rotation transformation formulas.
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 \(270\) degrees rotation, we first convert this angle to radians:
\[ \theta = 270^\circ = \frac{3\pi}{2} \text{ radians} \]
Now, we find the cosine and sine of \(270\) degrees:
\[ \cos(270^\circ) = 0 \] \[ \sin(270^\circ) = -1 \]
Substituting these values into the rotation formulas:
\[ x' = x \cdot 0 - y \cdot (-1) = y \] \[ y' = x \cdot (-1) + y \cdot 0 = -x \]
Thus, the new coordinates after rotating \((x, y)\) by \(270\) degrees counterclockwise are:
\[ (x', y') = (y, -x) \]
So the new point after the rotation is \((y, -x)\).