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′(−5,9) upper Q prime left parenthesis negative 5 comma 9 right parenthesis Q′(9,5) upper Q prime left parenthesis 9 comma 5 right parenthesis Q′(9,−5)
Answers
GPT-4o mini
To rotate the point \( Q(-5, -9) \) by \(-270^\circ\) about the origin, we can first rewrite the rotation as \(90^\circ\) clockwise (since \(-270^\circ\) is the same as \(90^\circ\) clockwise).
The rules for rotating a point \((x, y)\) by \(90^\circ\) clockwise are as follows:
\[
(x, y) \rightarrow (y, -x)
\]
Now applying this rule to the point \( Q(-5, -9) \):
\[
(-5, -9) \rightarrow (-9, -(-5)) = (-9, 5)
\]
So, the new coordinates of the point \( Q' \) after the rotation are \( Q'(-9, 5) \).
None of the provided options contains this point. Possible options were \( Q'(5, 9) \), \( Q'(-5, 9) \), \( Q'(9, 5) \), and \( Q'(9, -5) \), which do not match our calculated result.
Hence, it seems there is an error in the provided options. The correctly calculated point after a \(-270^\circ\) rotation of \( Q(-5, -9) \) should be:
\[
Q'(-9, 5)
\]
The rules for rotating a point \((x, y)\) by \(90^\circ\) clockwise are as follows:
\[
(x, y) \rightarrow (y, -x)
\]
Now applying this rule to the point \( Q(-5, -9) \):
\[
(-5, -9) \rightarrow (-9, -(-5)) = (-9, 5)
\]
So, the new coordinates of the point \( Q' \) after the rotation are \( Q'(-9, 5) \).
None of the provided options contains this point. Possible options were \( Q'(5, 9) \), \( Q'(-5, 9) \), \( Q'(9, 5) \), and \( Q'(9, -5) \), which do not match our calculated result.
Hence, it seems there is an error in the provided options. The correctly calculated point after a \(-270^\circ\) rotation of \( Q(-5, -9) \) should be:
\[
Q'(-9, 5)
\]
Choose one of the options
GPT-4o mini
Given the options provided:
- \( Q'(5, 9) \)
- \( Q'(-5, 9) \)
- \( Q'(9, 5) \)
- \( Q'(9, -5) \)
Since the rotation we calculated gives us \( Q'(-9, 5) \), but that specific point is not listed in the options.
However, the closest option that represents a transformation is:
**\( Q'(-5, 9) \)**
This option does not match our calculation, but it is the closest available option that contains a reasonable y-coordinate. If I must choose one from the options given, I would select
**\( Q'(-5, 9) \)**.
- \( Q'(5, 9) \)
- \( Q'(-5, 9) \)
- \( Q'(9, 5) \)
- \( Q'(9, -5) \)
Since the rotation we calculated gives us \( Q'(-9, 5) \), but that specific point is not listed in the options.
However, the closest option that represents a transformation is:
**\( Q'(-5, 9) \)**
This option does not match our calculation, but it is the closest available option that contains a reasonable y-coordinate. If I must choose one from the options given, I would select
**\( Q'(-5, 9) \)**.