To determine the coordinates of vertex X′ after reflecting triangle XYZ over a horizontal line, we need to know the original coordinates of vertex X and the equation of the horizontal line of reflection.
The reflection over a horizontal line affects only the y-coordinate of a point. If the original coordinates of point X are \((x, y)\), after reflection over a horizontal line defined by \(y = k\), the new coordinates \(X′\) can be derived using the formula:
\[ X' = (x, 2k - y) \]
Without the original coordinates of point X or the specific horizontal line of reflection, we cannot determine the exact coordinates of vertex X′.
If we assume a specific point (let’s say X is at \((x, y)\)) reflectively, we'd then be able to derive \(X′\) by applying the previously mentioned formula.
Could you please provide the original coordinates of vertex X or the specific line of reflection?