Question

Points P and Q belong to segment AB . If AB = a, AP = 2PQ = 2QB, find the distance between point A and the midpoint of the segment QB

Answer 1

A.........P.....Q.....B
So
AB=a,
AP=2PQ=2QB
so there are altogether 4 equal pieces, x, such that
AP=2x
PQ=x
QB=x
AB=4x=a => x=a/4

Midpoint of segment QB is x/2 from B, => 4x-x/2=(7/2)x from A.

Therefore midpoint of QB is (7/2)x=(7/2)(a/4)=(7/8)a from A.