Two lines PQ and ST intersect at 75∘ ∘ . The locus of points equidistant from PQ and ST lies on the

Two lines PQ and ST intersect at 75${}^{\circ }$. The locus of points equidistant from PQ and ST lies on the

Answer Details

The locus of points equidistant from two intersecting lines PQ and ST is the perpendicular bisector of the line segment joining PQ and ST. To understand why, consider a point P on line PQ and a point S on line ST. Let M be the midpoint of the line segment PS. Any point Q on line PQ that is equidistant from lines PQ and ST must be located on the perpendicular bisector of PS. Similarly, any point T on line ST that is equidistant from lines PQ and ST must also be located on the perpendicular bisector of PS. Therefore, the locus of points equidistant from lines PQ and ST lies on the perpendicular bisector of PS. Since the perpendicular bisector of PS is also the perpendicular bisector of line segment PQ and ST, option A (perpendicular bisector of PQ) is correct.