Given:
Segment AB has points A at (2,-5) and B at (5,-3)
Segment AB is reflected across the y - axis and then translated 3 units right.
We need to determine the coordinates of the endpoints on the image A'B'
Reflection across the y - axis:
The rule to reflect the coordinates across the y - axis is given by

Thus, the reflection of the point A is given by

The reflection of the point B is given by

Therefore, the reflection of the points A and B across the y - axis are (-2,-5) and (-5,-3) respectively.
Shifting 3 units to the right:
The rule to shift the coordinates to the right is given by

The point A is shifted 3 units to the right is given by

The point B is shifted 3 units to the right is given by

Hence, the coordinates of the endpoints on the image A' and B' are (1,-5) and (-2,-3)