Question

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)

Answer 1

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)