Question
The point Q(−5,−9) is rotated −270° about the origin. Select the location of Q′ . (1 point) Responses Q′(9,5) upper Q prime left parenthesis 9 comma 5 right parenthesis Q′(5,9) upper Q prime left parenthesis 5 comma 9 right parenthesis Q′(−5,9) upper Q prime left parenthesis negative 5 comma 9 right parenthesis Q′(9,−5)
Answers
GPT-4o mini
To find the coordinates of the point Q' after rotating the point Q(−5,−9) by −270° about the origin, we can follow the steps of rotation in the coordinate plane.
1. **Understanding the Rotation**: A rotation of −270° is equivalent to a rotation of 90° in the positive direction (since −270° + 360° = 90°).
2. **Applying the 90° Rotation Transformation**: The rule for rotating a point (x, y) by 90° counterclockwise around the origin is:
\[
(x, y) \rightarrow (-y, x)
\]
For the point Q(−5, −9):
- Here, x = -5 and y = -9.
- Applying the 90° rotation:
- New x-coordinate: -(-9) = 9
- New y-coordinate: -5
3. **Resulting Coordinates**: The new coordinates for Q′ after the rotation are (9, -5).
Thus, the location of Q' is:
\[
Q′(9, -5)
\]
So the correct response is: **Q′(9,−5)**.
1. **Understanding the Rotation**: A rotation of −270° is equivalent to a rotation of 90° in the positive direction (since −270° + 360° = 90°).
2. **Applying the 90° Rotation Transformation**: The rule for rotating a point (x, y) by 90° counterclockwise around the origin is:
\[
(x, y) \rightarrow (-y, x)
\]
For the point Q(−5, −9):
- Here, x = -5 and y = -9.
- Applying the 90° rotation:
- New x-coordinate: -(-9) = 9
- New y-coordinate: -5
3. **Resulting Coordinates**: The new coordinates for Q′ after the rotation are (9, -5).
Thus, the location of Q' is:
\[
Q′(9, -5)
\]
So the correct response is: **Q′(9,−5)**.