The length of a line segment remains unchanged after translation. Therefore, the length of line segment \(X'Y'\) would be the same as the length of line segment \(XY\).
To find the length of segment \(XY\), you'll need to know the coordinates of points \(X\) and \(Y\). The length can be calculated using the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Where \((x_1, y_1)\) are the coordinates of point \(X\) and \((x_2, y_2)\) are the coordinates of point \(Y\).
If you provide the coordinates of points \(X\) and \(Y\), I can calculate the length for you. If you just want to know the fact, the length of segment \(X'Y'\) will be the same as the length of segment \(XY\).