Question

The point Q (-5, -9) is rotated -270 degrees about the origin. Select the location of Q'.
A. Q' (5, 9)
B. Q' (-5, 9)
C. (9, -5)
D. (9, 5)

Answer 1

To determine the new location \( Q' \) after rotating point \( Q (-5, -9) \) by -270 degrees (which is equivalent to a +90 degrees rotation), we can use the following rules for rotation around the origin:

1. A point \( (x, y) \) rotated 90 degrees counterclockwise becomes \( (-y, x) \).
2. A point \( (x, y) \) rotated -270 degrees (or 90 degrees clockwise) becomes \( (y, -x) \).

Now applying the 90 degrees clockwise rule:

1. The original point is \( Q (-5, -9) \).
2. Applying the transformation:
- \( Q' = (-9, 5) \) because we swap the coordinates and change the sign of the x-coordinate.

The new location of \( Q' \) is therefore \( (-9, 5) \).

None of the provided options match this directly. Let's double-check the work:

1. Original point \( Q(-5, -9) \)
2. Rotate 90 degrees clockwise:
- New x-coordinate = -y = 9 (since y = -9)
- New y-coordinate = x = -5 (since x = -5)

So, \( Q' = (9, -5) \).

This corresponds to option **C. (9, -5)**.