The statement "No. You would need to know that overline NP≌ overline MN" is correct.
Given:
Point P lies on line segment LM.
Overline NL is perpendicular to overline LM.
This information alone is insufficient to conclude that point P lies on the perpendicular bisector of overline LM. The perpendicular bisector of a line segment is a line that passes through the midpoint of the line segment and is perpendicular to the line segment.
While we know that overline NL is perpendicular to overline LM, we don't have any information about the relative lengths of overline LP and overline MP. Knowing that overline NP≌ overline MN would ensure that point P is indeed the midpoint of line segment LM, and consequently, that overline NL is the perpendicular bisector of overline LM
Therefore, the statement "No. You would need to know that overline NP≌ overline MN" is correct. Knowing that overline NP≌ overline MN would conclusively establish that point P lies on the perpendicular bisector of overline LM.