To find the original coordinates of the endpoint before the translation, we need to reverse the translation process.
The line segment was translated 3 units down and 1 unit to the left. Thus, to find the original point, we need to do the opposite:
- Move 3 units up (to counteract the 3 units down).
- Move 1 unit to the right (to counteract the 1 unit to the left).
Starting with the coordinates (5, 8):
- Moving up 3 units: \(8 + 3 = 11\)
- Moving right 1 unit: \(5 + 1 = 6\)
So the original point before the translation is \((6, 11)\).
Thus, the answer is:
(6, 11)