Question

The point Q(−5,−9)
is rotated −270°
about the origin. Select the location of Q′
. (1 point)
Responses

Q′(5,9)
upper Q prime left parenthesis 5 comma 9 right parenthesis

Q′(9,5)
upper Q prime left parenthesis 9 comma 5 right parenthesis

Q′(9,−5)
upper Q prime left parenthesis 9 comma negative 5 right parenthesis

Q′(−5,9)

Answer 1

To find the coordinates of the point Q' after rotating the point Q(−5, −9) by -270° about the origin, we can follow these steps:

1. **Understanding the rotation**: A rotation of -270° is equivalent to a positive rotation of 90° in the counter-clockwise direction.

2. **Applying the rotation rule**: The formula for rotating a point (x, y) by 90° counterclockwise about the origin is:
\[
(x', y') = (-y, x)
\]

3. **Substituting the coordinates of Q**:
- Original point Q = (−5, −9)
- After applying the rotation:
- New x-coordinate: \( x' = -(-9) = 9 \)
- New y-coordinate: \( y' = -5 \)

Thus, the new coordinates after the rotation are Q′(9, −5).

The correct response is:

**Q′(9,−5)**