Question
The point Q(−5,−9)is rotated −270° about the origin. Select the location of Q′. (1 point)ResponsesQ′(9,−5)upper Q prime left parenthesis 9 comma negative 5 right parenthesisQ′(−5,9)upper Q prime left parenthesis negative 5 comma 9 right parenthesisQ′(9,5)upper Q prime left parenthesis 9 comma 5 right parenthesisQ′(5,9)
Answers
Answered by
GPT-4o mini
To rotate the point \( Q(-5, -9) \) by \(-270^\circ\) about the origin, we can first convert \(-270^\circ\) to a positive angle.
\[
-270^\circ + 360^\circ = 90^\circ
\]
Next, we'll use the rotation formula for a \(90^\circ\) counterclockwise rotation, which transforms the coordinates \( (x, y) \) as follows:
\[
(x, y) \to (-y, x)
\]
Now, substituting the coordinates of point \( Q(-5, -9) \):
\[
Q(-5, -9) \to (-(-9), -5) = (9, -5)
\]
Thus, the location of \( Q' \) after the rotation is:
\[
Q'(9, -5)
\]
So the correct response is:
**Q′(9,−5)**
\[
-270^\circ + 360^\circ = 90^\circ
\]
Next, we'll use the rotation formula for a \(90^\circ\) counterclockwise rotation, which transforms the coordinates \( (x, y) \) as follows:
\[
(x, y) \to (-y, x)
\]
Now, substituting the coordinates of point \( Q(-5, -9) \):
\[
Q(-5, -9) \to (-(-9), -5) = (9, -5)
\]
Thus, the location of \( Q' \) after the rotation is:
\[
Q'(9, -5)
\]
So the correct response is:
**Q′(9,−5)**
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