Question

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

(x,y) →
(-y, x)
(x,y) right arrow (-y, x)

(x,y) →
(y, x)
(x,y) right arrow (y, x)

(x,y) →
(x, -y)
(x,y) right arrow (x, -y)

(x,y) →
(2x, 2y)
(x,y) right arrow (2x, 2y)

Answer 1

To determine the rotation function mapping that transforms the point A (-7, 4) to the point A' (-4, -7), we can analyze the coordinates.

- The original point A is (-7, 4).
- The transformed point A' is (-4, -7).

A rotation gives us a relationship between the coordinates. Specifically, a rotation in the counterclockwise direction of 90 degrees can be represented by the transformation:

\[
(x, y) \rightarrow (-y, x)
\]

Let's apply this transformation to point A:

1. Start with A: (-7, 4).
2. Apply the transformation:
\[
(-y, x) = (-4, -7)
\]

As we can see, applying this transformation results in the desired point A' (-4, -7).

Therefore, the correct rotation function mapping used to turn A (-7, 4) into A' (-4, -7) is:

\[
(x, y) \rightarrow (-y, x)
\]

Thus, the correct response is:

**(x,y) → (-y, x)**