Question

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

Answer 1

Since PQ = QB, PB = 2PQ = AP. Thus P is the midpoint of AB, and Q is the midpoint of PB. Then the midpoint (X) of QB is AP + PQ + QX = 1/2 + 1/4 + 1/8 times the length of AB from A.

The distance from A to the midpoint of QB is (7/8)a.