The information on the figure is NOT enough to conclude whether point P is a perpendicular bisector of LM
What is a perpendicular bisector
A perpendicular bisector is a line or line segment that both bisects a given segment (divides LM into two equal parts) and is perpendicular (forms a right angle) to that segment (LM).
From the definition we can pick that
- divides LM into two equal parts
The information showed that line PN is perpendicular to LN. that is forms right angle. However, no information about bisecting line LM or dividing line LM into 2 equal parts
Hence we say that the information is not sufficient to ascertain if line PN is the perpendicular bisector