Final answer:
In a geometry problem where PQ is the perpendicular bisector of MN, MP is equal to half the length of MN because a perpendicular bisector divides a segment into two equal parts.
Step-by-step explanation:
The question presented is a geometry problem where PQ is the perpendicular bisector of MN.
In geometry, a perpendicular bisector is a line which cuts a line segment into two equal parts at a 90-degree angle. Since PQ bisects MN, it tells us that MP is equal to NP, which are the segments from M to the bisecting point P, and from N to P, respectively.
Therefore, MP is equal to half the length of MN. To find MP, you must measure the length of MN and then divide it by two.