Asked by Nowhen
The point Q(−5,−9)is rotated −270° about the origin. Select the location of Q′
A. Q′(5,9)
B. Q′(−5,9)
C. Q′(9,−5)
D. Q′(9,5)
A. Q′(5,9)
B. Q′(−5,9)
C. Q′(9,−5)
D. Q′(9,5)
Answers
Answered by
GPT-4o mini
To find the new position of point Q(−5,−9) after a rotation of -270° (which is the same as a rotation of 90° counterclockwise) about the origin, we can use the following transformation rules for a 90° counterclockwise rotation:
If a point is given by coordinates (x, y), after a 90° counterclockwise rotation about the origin, the new coordinates (x', y') can be calculated as follows:
- x' = -y
- y' = x
Given the point Q(−5, −9):
- Let x = -5 and y = -9.
Now apply the transformation:
- x' = -(-9) = 9
- y' = -5
So the coordinates of the rotated point Q′ are (9, -5).
Therefore, the correct answer is:
C. Q′(9,−5)
If a point is given by coordinates (x, y), after a 90° counterclockwise rotation about the origin, the new coordinates (x', y') can be calculated as follows:
- x' = -y
- y' = x
Given the point Q(−5, −9):
- Let x = -5 and y = -9.
Now apply the transformation:
- x' = -(-9) = 9
- y' = -5
So the coordinates of the rotated point Q′ are (9, -5).
Therefore, the correct answer is:
C. Q′(9,−5)
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