Moving a line segment is equivalent to moving its endpoints.
When a point (x0,y0) is rotated about the origin by π2, the new point is always (x1,y1)=(-y0,x0). Think of it like this: if you're walking in the woods and holding a map so that "forward" is east, that's the same situation. The map's "right" (east) is your "forward", the map's "forward" (north) is your "left", etc.
So in a 1/4 turn counterclockwise, old right (x0) becomes new up (y1), and old up (y0) becomes new left (-x1). This is the same as (x1,y1)=(-y0,x0).
So after rotating our points π2 about the origin, the new points are:
(-4,7) and (-5,2).
Horizontal translations only affect your x-value, because they are a left-right (x-axis) shift, and not an up-down (y-axis) shift.
After translating both points horizontally by -3, our new points are:
(-7,7) and (-8,2).
Finally, reflecting a point about the y-axis simply means changing the sign of its x-coordinate. This reflection is a left-to-right flip, so the up-down (y) location will not change. (If you flip a map over so that north and south stay "up" and "down", the map's "east" becomes left, and its "west" becomes right.)
After reflection about the y-axis, our final points will be:
(7,7) and (8,2).
