To find the rotation function that maps point A (-7, 4) to A' (-4, -7), we can analyze the transformation of the coordinates through each given option.
- Original Point A = (-7, 4)
- Transformed Point A' = (-4, -7)
Let's examine the options:
A. (x,y) → (2x, 2y)
This multiplies both coordinates by 2.
For A (-7, 4):
(2*(-7), 2*4) = (-14, 8) which does not match A'.
B. (x,y) → (-y, x)
This switches and negates the x-coordinate with the y-coordinate.
For A (-7, 4):
(-4, -7) which matches A'.
C. (x,y) → (x, -y)
This negates the y-coordinate.
For A (-7, 4):
(-7, -4) which does not match A'.
D. (x,y) → (y, x)
This switches the x and y coordinates.
For A (-7, 4):
(4, -7) which does not match A'.
The option B transformation, which is (x,y) → (-y, x), successfully maps point A (-7, 4) to point A' (-4, -7).
Therefore, the correct answer is B. (x,y) → (-y, x).