Question

Identify the rotation function mapping used to turn A (-7,4) to A'(-4, -7). A:(x,y) (-y,x)
B: (x,y) (y -x) C: (x,y) (-y, -x)

Answer 1

To find the rotation function that maps point A (-7, 4) to point A' (-4, -7), we can analyze the options given:

Let's evaluate each rotation function:

1. **A: (x, y) → (-y, x)**
- Applying this to A (-7, 4):
\[
(-y, x) = (-4, -7)
\]
This function rotates the point 90 degrees counterclockwise.

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

3. **C: (x, y) → (-y, -x)**
- Applying this to A (-7, 4):
\[
(-y, -x) = (-4, 7)
\]
This is a 180-degree rotation, but it also does not match A'.

Based on this analysis, the only function that correctly maps A to A' is function **A: (x, y) → (-y, x)**, which represents a 90-degree counterclockwise rotation.

Thus, the answer is **A: (x, y) → (-y, x)**.