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

Question

Responses

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

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

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

(x,y) → (2x, 2y)

Answer 1

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

The transformation from A to A' can be observed as follows:

• The x-coordinate of A (-7) becomes the y-coordinate of A' (-4).
• The y-coordinate of A (4) becomes the negation of the x-coordinate of A' (-7), meaning it moves to the x-axis.

This indicates a 90-degree counterclockwise rotation around the origin, which corresponds to the mapping:

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

Therefore, the correct answer is:

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