To determine the coordinates of vertex \( X' \) after triangle \( XYZ \) is reflected over a horizontal line, we first need to know the coordinates of vertex \( X \) and the y-coordinate of the line of reflection.
Assuming:
- The coordinates of vertex \( X \) are \( (x, y) \).
- The equation of the horizontal line of reflection is \( y = k \) (where \( k \) is the y-coordinate of the line).
The reflection of a point \( (x, y) \) over the line \( y = k \) is found by calculating the new y-coordinate as follows:
- Find the vertical distance from point \( X \) to the line of reflection: \( d = y - k \).
- Since reflection will place the point the same distance on the opposite side of the line, the new y-coordinate \( y' \) will be: \[ y' = k - d = k - (y - k) = 2k - y \]
- The x-coordinate remains unchanged.
Thus, the coordinates of vertex \( X' \) after reflection will be: \[ X' = (x, 2k - y) \]
If you provide the coordinates of vertex \( X \) and the line of reflection, I can give you the specific coordinates of \( X' \).
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