Point P is taken on line AB, find the distance between the midpoints of the segments AP and PB, if AB = 20 cm, BP = 30 cm.

Given:
segment AB,
point M is the middle of AP,
point K is the middle of PB,
AB = 20 centimeters,
BP = 30 centimeters,
point P is located behind point B.
Find the length of the segment MK -?
Solution:
1) Consider the segment AB.
AR = AB + PB;
AR = 20 + 30;
AP = 50;
2) AM = MP = 50: 2;
AM = MR = 25 centimeters;
3) ВK = KР = 30: 2;
ВK = KR = 15 centimeters;
4) MK = MР – KР;
MK = 25 – 15;
MK = 10 centimeters.
Answer: 10 centimeters.