To rotate a point \((x, y)\) counterclockwise about the origin by an angle of 270 degrees, you can use the rotation formula. The rotation of a point \((x, y)\) counterclockwise by an angle \(\theta\) is given by the following formulas:
\[ x' = x \cdot \cos(\theta) - y \cdot \sin(\theta) \] \[ y' = x \cdot \sin(\theta) + y \cdot \cos(\theta) \]
For a rotation of 270 degrees:
- \(\cos(270^\circ) = 0\)
- \(\sin(270^\circ) = -1\)
Substituting these values into the formulas gives:
\[ x' = x \cdot 0 - y \cdot (-1) = y \] \[ y' = x \cdot (-1) + y \cdot 0 = -x \]
Therefore, the new point after rotating \((x, y)\) counterclockwise by 270 degrees is:
\[ (y, -x) \]
So the new point is \((y, -x)\).