To find the rotation function mapping that turns point \( A(-7, 4) \) into point \( A'(-4, -7) \), we can analyze how the coordinates change.
The original point is \( A(-7, 4) \). The new point is \( A'(-4, -7) \).
Let's denote the transformation as \( (x, y) \rightarrow (x', y') \):
- The first coordinate transformation is from \( -7 \) to \( -4 \).
- The second coordinate transformation is from \( 4 \) to \( -7 \).
Let's see how the transformation matches one of the given functions:
-
Option \( (x, y) \rightarrow (y, -x) \):
- Apply this to \( (-7, 4) \):
- \( x' = 4 \), \( y' = -(-7) = 7 \) (not a match).
-
Option \( (x, y) \rightarrow (-y, x) \):
- Apply this to \( (-7, 4) \):
- \( x' = -4 \), \( y' = -7 \) (this matches the new point \( A'(-4, -7) \)).
-
Option \( (x, y) \rightarrow (-x, -y) \):
- Apply this to \( (-7, 4) \):
- \( x' = 7 \), \( y' = -4 \) (not a match).
-
Option \( (x, y) \rightarrow (-y, -x) \):
- Apply this to \( (-7, 4) \):
- \( x' = -4 \), \( y' = 7 \) (not a match).
The correct option that represents the rotation function is:
\( (x, y) \rightarrow (-y, x) \).