To find the length of line segment XY after it has been translated to form line segment X'Y', we first need to determine the length of the original line segment XY.
The length of a line segment can be calculated using the distance formula, which is given by:
\[ L = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
where \((x_1, y_1)\) are the coordinates of point X, and \((x_2, y_2)\) are the coordinates of point Y.
Translation of the line segment does not change its length, only its position. Therefore, the length of line segment X'Y' after the translation is the same as the length of line segment XY.
Since you haven't provided the coordinates of points X and Y, I can't compute the specific length. However, I can assure you that the length of line segment X'Y' will be equal to the length of line segment XY.
If you provide the coordinates, I can assist you in calculating the actual length.