To find the coordinates of point F' after a reflection across the line \( x = -1 \), we need to determine the position of point F before the reflection, but since the options don't provide the original coordinates of point F, let's describe how to derive the coordinates for F' after reflecting a point (x_F, y_F) across the line \( x = -1 \).
- Identify the x-coordinate of point F, let's call it \( x_F \).
- The line \( x = -1 \) is vertical. To find the reflected point F', we need to find how far point F is from the line.
- The distance from F to the line is \( x_F - (-1) = x_F + 1 \).
- To reflect F, we move the same distance to the left of the line \( x = -1 \):
- The new x-coordinate becomes: \[ x' = -1 - (x_F + 1) = -1 - x_F - 1 = -x_F - 2 \]
For point F' to be one of the given options, we assume one of those points could have been derived by reflecting some point F across \( x = -1 \).
Let's test the provided options to check which could possibly be the result of reflecting across \( x = -1 \):
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F'(-1, 4): This means F must have been at (-1, 4) pre-reflection, which does not change - this is a vertical line from itself, does not correspond to any reflection.
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F'(3, 5): If F' is at (3, 5), after reflection F should be at (-5, 5). This is valid as distance of 4 units to the right of x=-1 gets translated to -5 as point reflection.
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F'(5, -5): F would have been at (-7, -5). This would be reflected across x=-1 to reach 5, -5. Again valid across distance.
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F'(-5, -5): Similar reasoning goes as this requires a point of (-3, -5) which does not resolve valid reflection process.
Based on this analysis, F'(3, 5) appears to be the valid reflection result where x-coordinates make sense based on distance across the -1 vertical line.
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