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:
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Distance from F to the line x = -1:
- The x-coordinate of F is -5. The distance from -5 to -1 is: \[ |-5 - (-1)| = |-5 + 1| = |-4| = 4 \]
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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: \[ -1 + 4 = 3 \]
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Keeping the y-coordinate the same, the reflected point F' will have the same y-coordinate as F. Thus:
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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.
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