Question

The point Q(-5, -9) is rotated -270 degrees about the origin. Select the location of Q'.
A. Q' (5, 9)
B. Q' (-5, 9)
C. (9, -5)
D. (9, 5)

Answer 1

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 \(Q(-5, -9)\):

1. Set \(x = -5\) and \(y = -9\).
2. 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 \((-9, 5)\).