We call the points x and y. The locus is the perpendicular bisector of the segment xy.
Work Step by Step
Recall, a locus is equidistant from the points no matter where you are. Therefore, first construct the original points. Then, draw a line (which is red in the diagram) that is the same distance from the original line at all points. A theorem states that the locus of two points is the perpendicular bisector of the segment that joins the points.