Geometrically, to "reflect" a point in a line you draw a perpendicular to the line and find the point on the other side of the line, on that perpendicular, at the same distance from the line. Another way of saying that is that the midpoint of the line segment between the two points is on the given "reflecting" line.
Since this is x= 1/2 a perpendicular line has constant y. If the given point is (a, b) the reflected point must be of the form (x, b) and we must have (a+x)/2= 1/2. then a+ x= 1 so x= 1- a. The point (a, b) reflects to (1-a, b).