To rotate a point around the origin, we can use the formula for rotating a point \((x, y)\) by an angle \(\theta\).
A rotation of \(-270\) degrees is equivalent to a rotation of \(90\) degrees clockwise (since \(-270 + 360 = 90\)).
The rotation formulas are as follows:
- For a rotation of \(90^\circ\) clockwise: \[ (x', y') = (y, -x) \]
Now, let's apply this to point \(Q(-5, -9)\):
- Set \(x = -5\) and \(y = -9\).
- Apply the rotation formula: \[ x' = y = -9 \] \[ y' = -x = -(-5) = 5 \]
So the rotated coordinates \(Q'\) will be: \[ Q'(-9, 5) \]
Now, looking at the answer choices provided:
- A. Q' (5, 9)
- B. Q' (-5, 9)
- C. (9, -5)
- D. (9, 5)
None of the choices match the calculated result of \((-9, 5)\). It seems there might be an error in the provided options. Please verify the options or the rotation. However, according to our calculation, the rotated coordinates of \(Q\) after a \(-270^\circ\) rotation would be \((-9, 5)\).
1 answer