Final answer:
The endpoints of the segment after reflecting over the y-axis are A'(-2,4) and B'(-4,0).
Step-by-step explanation:
To find the endpoints of the image after reflecting the segment AB over the y-axis, we need to change the sign of the x-coordinate of each point. So, the x-coordinate of point A becomes positive and the x-coordinate of point B becomes negative. Using this rule, the endpoints of the reflected segment are A'(-2,4) and B'(-4,0).