Question

For AFUN, x = -1. What are the
coordinates for F" after a reflection?
(1 point)
O F' (5, -5)
• F' (3,5)
OF' (-1,4)
О F' (-5, -5)

F is -5,5
U is -1,4
N is -3,0

Answer 1

To determine the coordinates of the reflection of point F after reflection across the line defined by AFUN where A is (-1, 4), F is (-5, 5), U is (-1, 4), and N is (-3, 0), we first need to understand the situation regarding the reflection.

Given the coordinates:
- F(-5, 5)
- U(-1, 4) (but it appears U is the line of reflection in this case)

### Reflecting point F across the line y = mx + b

In this scenario, the line of reflection appears to be vertical (since it’s described by the constant x = -1, reflecting horizontally), thus:

1. **Distance from F to the line x = -1**:
- The x-coordinate of F is -5. The distance from -5 to -1 is:
\[
|-5 - (-1)| = |-5 + 1| = |-4| = 4
\]

2. **Finding the reflected coordinate**:
- The reflection across x = -1 would occur on the opposite side. Therefore, we add 4 to -1 to find the reflected x-coordinate:
\[
-1 + 4 = 3
\]

3. **Keeping the y-coordinate the same**, the reflected point F' will have the same y-coordinate as F. Thus:

4. The new coordinates will be:
\[
F' = (3, 5)
\]

Hence, the coordinates of F' after the reflection about the line x = -1 are **F' (3, 5)**. This matches one of the provided options.

### Answer: F' (3, 5)