Points on line segment

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

Result

x =  0.8 a

Solution:

a=1 a1=1/(1+2+2)=15=0.2 x=(1+2+2/2)⋅ a1=(1+2+2/2)⋅ 0.2=45=0.8=0.8  a a = 1 \ \\ a_{ 1 } = 1/(1+2+2) = \dfrac{ 1 }{ 5 } = 0.2 \ \\ x = (1+2+2/2) \cdot \ a_{ 1 } = (1+2+2/2) \cdot \ 0.2 = \dfrac{ 4 }{ 5 } = 0.8 = 0.8 \ \text{ a }

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