Question

*Line segment AB is divided into 4 unequal parts by points C, D, and E (in this order). The distance between midpoints of segments AC and EB is 30 cm. Find the distance between the midpoints of segments CD and DE , if AB = 36 cm.

Answer 1

Let X and Y represent the midpoints of AC and EB, respectively. We are given

AB = 36

XY = 30

We know that AX +XY +YB = AB = 36, so AX+YB = 36-30 = 6. We also know that AX = XC and EY = YB, so XC+EY = AX+YB = 6.

Since XC +CE + EY = XY = 30, and XC+EY = 6, we must have CE = 30-6 = 24.

The distance between the midpoints of CD and DE will be half the length of CE, so will be 12 cm.