To rotate a point \((-5, -9)\) around the origin, we can use the rotation transformation formula. Rotating a point \((x, y)\) by an angle \(\theta\) (in degrees) around the origin can be expressed with the following formulas:
\[ x' = x \cos(\theta) - y \sin(\theta) \] \[ y' = x \sin(\theta) + y \cos(\theta) \]
For \(-270^\circ\), we can express it in terms of a positive angle: \[ -270^\circ = 90^\circ \]
So, we need to use \(\theta = 90^\circ\): \[ \cos(90^\circ) = 0, \quad \sin(90^\circ) = 1 \]
Now, applying the formulas to the point \(Q(-5, -9)\):
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Calculate \(x'\): \[ x' = -5 \cdot 0 - (-9) \cdot 1 = 0 + 9 = 9 \]
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Calculate \(y'\): \[ y' = -5 \cdot 1 + (-9) \cdot 0 = -5 + 0 = -5 \]
Thus, the coordinates after the rotation are: \[ Q' = (9, -5) \]
Therefore, the correct answer is: C. \(Q' (9, -5)\).