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)