Question

Identify the rotation function mapping used to turn A (-7, 4) to A' (-4, -7). (1 point)
(x,y) → (x, -y)
(x,y) → (-y, x)
(x,y) → (2x, 2y)
(x,y) → (y, x)

Answer 1

To determine the appropriate rotation function mapping used to turn the point A (-7, 4) into the point A' (-4, -7), we can analyze each of the given options.

1. \( (x,y) \to (x, -y) \)
- Applying this to A:
\[
(-7, 4) \to (-7, -4)
\]
- This does not match A'.

2. \( (x,y) \to (-y, x) \)
- Applying this to A:
\[
(-7, 4) \to (-4, -7)
\]
- This matches A'!

3. \( (x,y) \to (2x, 2y) \)
- Applying this to A:
\[
(-7, 4) \to (-14, 8)
\]
- This does not match A'.

4. \( (x,y) \to (y, x) \)
- Applying this to A:
\[
(-7, 4) \to (4, -7)
\]
- This does not match A'.

From this analysis, the function that correctly transforms A (-7, 4) to A' (-4, -7) is:

**Answer:** \( (x,y) \to (-y, x) \)