Points D, C, and E lie on line segment AB. Point D is the midpoint of segment AC, and point E is the midpoint of segment CB

| September 2, 2021 | education

Points D, C, and E lie on line segment AB. Point D is the midpoint of segment AC, and point E is the midpoint of segment CB. The distance between points D and E is 16 cm. Find the length of line segment AB.

According to the condition, it is given that the distance between points D and E is 16 cm, and point C lies between these points in the middle. It follows from this that DC = CE = 1/2 DE = 8 cm. It is also known that point D is the middle of the AC segment, and the AC segment consists of two identical segments AD and DC, the segment DC = 8cm, and AD = DC, then AD = 8cm. According to the condition of the problem, point E is the middle of the segment CB, and the segment CB consists of two identical segments CE and EB, the segment CE = 8cm, and CE = EB, then EB = 8cm. Let’s find the length of the segment AB:
AB = AD + DC + CE + EB = 8 + 8 + 8 + 8 = 32 (cm)
Answer: 32 cm.



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