Question
The point Q(-5,-9) is rotated -270 degrees about the origin. Select the location of Q'.
(9,-5)
(9,-5)
(9,5)
(9,5)
(-5, 9)
(-5, 9)
(5,9)
(9,-5)
(9,-5)
(9,5)
(9,5)
(-5, 9)
(-5, 9)
(5,9)
Answers
GPT-4o mini
To find the new coordinates \( Q' \) after rotating the point \( Q(-5, -9) \) by -270 degrees (which is equivalent to a +90 degree rotation), we can use the following rotation formula for a point \( (x, y) \) around the origin:
\[
(x', y') = (y, -x)
\]
For point \( Q(-5, -9) \):
- \( x = -5 \)
- \( y = -9 \)
After applying the rotation:
\[
x' = y = -9
\]
\[
y' = -x = -(-5) = 5
\]
So, the new coordinates \( Q' \) are:
\[
Q'(-9, 5)
\]
Now we can match it with the given options:
- (9, -5)
- (9, 5)
- (-5, 9)
- (5, 9)
None of the options provided match the coordinates we calculated for \( Q' \).
Please double-check the provided options, as it seems there might be a discrepancy. The correct coordinates after the -270 degree rotation should be (-9, 5).
\[
(x', y') = (y, -x)
\]
For point \( Q(-5, -9) \):
- \( x = -5 \)
- \( y = -9 \)
After applying the rotation:
\[
x' = y = -9
\]
\[
y' = -x = -(-5) = 5
\]
So, the new coordinates \( Q' \) are:
\[
Q'(-9, 5)
\]
Now we can match it with the given options:
- (9, -5)
- (9, 5)
- (-5, 9)
- (5, 9)
None of the options provided match the coordinates we calculated for \( Q' \).
Please double-check the provided options, as it seems there might be a discrepancy. The correct coordinates after the -270 degree rotation should be (-9, 5).