The locus in a plane is two more intersecting lines, perpendicular to each other (and of course half-way between the given lines.
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The locus of a moving point so that it is equidistant from another fixed point (i.e. the distance between them is always constant) is a circle.
The locus point is the perpendicular bisector of AB. The locus point is the perpendicular bisector of AB.
A Circle.