To rotate a point counterclockwise about the origin, you can use the rotation transformation formulas. A rotation of \( \theta \) degrees can be done using 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 (which is equivalent to -90 degrees), the cosine and sine values are:
\[ \cos(270^\circ) = 0 \] \[ \sin(270^\circ) = -1 \]
Now, applying these values to the point \((-4, 5)\):
\[ x' = -4 \cdot 0 - 5 \cdot (-1) = 0 + 5 = 5 \] \[ y' = -4 \cdot (-1) + 5 \cdot 0 = 4 + 0 = 4 \]
Thus, the new point after rotating \((-4, 5)\) counterclockwise about the origin by 270 degrees is:
\[ (5, 4) \]