To rotate a point \((x, y)\) counterclockwise about the origin by an angle \(\theta\), you can use the rotation formulas:
\[ x' = x \cos(\theta) - y \sin(\theta) \] \[ y' = x \sin(\theta) + y \cos(\theta) \]
In this case, the angle \(\theta\) is 270 degrees. First, we need to convert 270 degrees to radians:
\[ 270^\circ = \frac{3\pi}{2} \text{ radians} \]
Now, we find the cosine and sine of \(270^\circ\):
\[ \cos(270^\circ) = 0 \] \[ \sin(270^\circ) = -1 \]
Now, substitute the point \((-4, 5)\) into the rotation formulas:
\[ x' = -4 \cdot 0 - 5 \cdot (-1) = 0 + 5 = 5 \] \[ y' = -4 \cdot (-1) + 5 \cdot 0 = 4 + 0 = 4 \]
Thus, the new point after a 270 degree counterclockwise rotation is:
\[ (5, 4) \]
So, the final answer is \((5, 4)\).
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