To rotate a point \((x, y)\) by an angle \(\theta\) counterclockwise about the origin, you can use the following transformation: \[ (x', y') = (x \cos \theta - y \sin \theta, x \sin \theta + y \cos \theta) \]
For a rotation of 270 degrees counterclockwise, we have: \[ \theta = 270^\circ \] The cosine and sine of 270 degrees are: \[ \cos(270^\circ) = 0 \quad \text{and} \quad \sin(270^\circ) = -1 \]
Now, substituting \((x, y) = (5, 8)\): \[ x' = 5 \cdot 0 - 8 \cdot (-1) = 0 + 8 = 8 \] \[ y' = 5 \cdot (-1) + 8 \cdot 0 = -5 + 0 = -5 \]
Thus, the new point after the rotation is: \((8, -5)\)
So, the correct answer is: \((8, -5)\)