Geometry

I have another question that stumped me

Line segment AB with length a is divided by points P and Q into three line segments: AP , PQ, and QB , such that AP = 2PQ=2QB. Find:
A)the distance between point A and the midpoints of the segments the segment QB
B) the distance between the midpoints of segments AP and QB.

I don't get what this question wants from me can you please describe the proces and the steps for this question
Thanks
:)

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asked by Ava
  1. You know that

    AP+PQ+QB = a

    Now, AP = 2PQ = 2BQ
    That means that PQ = QB and that gives us

    2PQ + PQ + PQ = a
    4PQ = a
    PQ = a/4

    Let M be the midpoint of QB
    Let N be the midpoint of AP
    AM = AP+PQ+ QB/2
    = a/2 + a/4 + a/8 = 7a/8
    NM = AP/2 + PQ + QB/2
    = a/4 +a/4 + a/8 = 5a/8

    Draw and label the line segment AB and you can see this is true.

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    posted by Steve

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