Question

Identify the rotation function mapping used to turn A(−7,4)
to A′(−4,−7)
.(1 point)
Responses

(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)
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 negative x right parenthesis

(x,y)→(−y,x)

Answer 1

To identify the rotation function mapping that takes the point A(−7, 4) to A′(−4, −7), we can analyze the change in coordinates.

Starting point:
- A(−7, 4)

Ending point:
- A′(−4, −7)

Now, let's check how the coordinates change:

1. The x-coordinate changes from -7 to -4.
2. The y-coordinate changes from 4 to -7.

The transformation can be represented as follows:
- The new x-coordinate (A′_x) is the negative of the y-coordinate of the original point (A_y): A′_x = -y → -4 = -4.
- The new y-coordinate (A′_y) is the negative of the x-coordinate of the original point (A_x): A′_y = -x → -7 = -(-7).

This indicates that the mapping is:
\[
(x, y) \rightarrow (-y, x)
\]

Thus, the correct response is:
\[
\text{(x,y)→(−y,x)}
\]