To determine the coordinates of the point F' after a reflection across the line x = -1, we first need to understand how reflections work with respect to this vertical line.
When reflecting a point (x, y) across the line x = -1:
- Take the original x-coordinate and find its distance to the line x = -1.
- Move the same distance to the other side of the line.
Let's denote the original point F as (x, y). If x = -1, F is on the line and will remain the same after reflection (F' = F). However, if we consider points not on the line x = -1, we will reflect accordingly.
If we take an original point, let's say F is (x, y), where x is any value not equal to -1:
- For any point F, the distance from x to -1 is |-1 - x|.
- To find F', we would have to go the same distance on the opposite side by using the equation: x' = -1 - (x + 1) = -2 - x.
Given the options and that we want to find the correct option that corresponds to the point reflection across x = -1:
For example, let’s reflect common coordinates:
- If the original point is (5, -5):
- Distance from -1: 5 - (-1) = 6 → F' would be (-1 - 6, -5) = (-7, -5) (not an option).
- If the original point is (3, 5):
- Distance from -1: 3 - (-1) = 4 → F' would be (-1 - 4, 5) = (-5, 5) (not an option).
- If the original point is (-1, 4):
- Distance from -1 is 0 → F' will be (-1, 4) (same point).
- If the original point is (-5, -5):
- Distance from -1: -5 - (-1) = -4 → F' would be (-1 + 4, -5) = (3, -5) (not an option).
After analyzing all these transformations based on the options:
The only reasonable option that results from the transformation or remains valid would be from the given F, which is F' = F (if the original was indeed at x = -1).
Since none reflect the manner outlined, I will select the valid representative:
The answer seems most closely associated with "F' (-1, 4)" as it mirrors clearly across x = -1. Thus, overall, we conclude:
Response: F' (-1, 4).