Question

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

Answer 1

To find the coordinates of \( F' \) after a reflection across the line \( x = -1 \), we follow these steps:

1. Determine the original coordinates of point \( F \) (if not provided, it must be derived from options).
2. Reflect \( F \) across the line \( x = -1 \).

Let's assume \( F \) has coordinates \( (a, b) \). The formula for reflecting a point \( (x, y) \) across the line \( x = k \) is given by:

\[
x' = 2k - x
\]
\[
y' = y
\]

For our case, \( k = -1 \), so the reflection formula becomes:

\[
x' = 2(-1) - a = -2 - a
\]
\[
y' = b
\]

Now, we can check the given options to determine which point yields a correct reflection based on \( x = -1 \):

1. If \( F = (5, -5) \):
\[
x' = -2 - 5 = -7 \quad (not \; a \; match)
\]

2. If \( F = (-1, 4) \):
\[
x' = -2 - (-1) = -2 + 1 = -1 \quad (no \; change \; in \; position)
\]

3. If \( F = (3, 5) \):
\[
x' = -2 - 3 = -5
\]
\[
y' = 5 \quad \text{So, } F' = (-5, 5) \quad (not \; a \; match)
\]

4. If \( F = (-5, -5) \):
\[
x' = -2 - (-5) = -2 + 5 = 3
\]
\[
y' = -5 \quad \text{So, } F' = (3, -5) \quad (not \; a \; match)
\]

After evaluating all points, the correct reflection cannot be fully determined without details on \( F \). Nonetheless, it appears:

1. For **F' = (3, 5)**, it could be derived from F being reflected across \( x = -1 \).

Therefore, without the original coordinates of \( F \), let’s say the answer from the equation gives \( F' = (3, 5) \) as a possible outcome.

Thus, **the best reasonable answer is:**

**F' = (3, 5)**.