dentify the rotation function mapping used to turn A(−7,4)

Question

to A′(−4,−7)
.(1 point)
Responses

(x,y)→(y,−x)
left parenthesis x comma y right parenthesis right arrow left parenthesis y comma negative x right parenthesis

(x,y)→(−y,x)
left parenthesis x comma y right parenthesis right arrow left parenthesis negative y comma x right parenthesis

(x,y)→(−x,−y)
left parenthesis x comma y right parenthesis right arrow left parenthesis negative x comma negative y right parenthesis

(x,y)→(−y,−x)

Answer 1

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:

1. Option \( (x, y) \rightarrow (y, -x) \):

   • Apply this to \( (-7, 4) \):
   • \( x' = 4 \), \( y' = -(-7) = 7 \) (not a match).

2. Option \( (x, y) \rightarrow (-y, x) \):

   • Apply this to \( (-7, 4) \):
   • \( x' = -4 \), \( y' = -7 \) (this matches the new point \( A'(-4, -7) \)).

3. Option \( (x, y) \rightarrow (-x, -y) \):

   • Apply this to \( (-7, 4) \):
   • \( x' = 7 \), \( y' = -4 \) (not a match).

4. 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:

\( (x, y) \rightarrow (-y, x) \).