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 negative 5 right parenthesis 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)
Answers
GPT-4o mini
To rotate the point Q(−5,−9) by -270° (which is equivalent to +90°), we can use the rotation transformation formulas for rotating a point (x, y) about the origin by an angle θ:
1. When rotating by +90°:
\[
(x, y) \rightarrow (-y, x)
\]
Applying this to the point Q(−5,−9):
- x = -5
- y = -9
Now, substituting into the formula:
\[
(-y, x) \rightarrow (9, -5)
\]
Thus, the rotated point Q′ will be (9, -5).
The correct response is:
**Q′(9,−5)**.
1. When rotating by +90°:
\[
(x, y) \rightarrow (-y, x)
\]
Applying this to the point Q(−5,−9):
- x = -5
- y = -9
Now, substituting into the formula:
\[
(-y, x) \rightarrow (9, -5)
\]
Thus, the rotated point Q′ will be (9, -5).
The correct response is:
**Q′(9,−5)**.