AB = 1, A(a1,a2), B(b1,b2)

M1 is the midpoint of AB thus the coordinates of M1 are

m11 = (a1 + b1)/2

m12 = (a2 + b2)/2

M2 is the midpoint of M1 and B the the coordinates of M2 are

m21 = (m11 + b1)/2 = (a1 + b1)/4 + b1/2

m22 = (m12 + b2)/2 = (a2 + b2)/4 + b2/2

M3 is the midpoint of M2 and B the the coordinates of M3 are

m31 = (m21 + b1)/2 = (a1 + b1)/8 + b1/4 + b1/2

m32 = (m22 + b2)/2 = (a2 + b2)/8 + b2/4 + b2/2

the coordinates of Mn will be

mn1 = (a1 + b1)/(2^n) + b1/(2^(n-1)) + ... + b1/2

mn2 = (a2 + b2)/(2^n) + b2/(2^(n-1)) + ... + b2/2

for n = 7 we have

m71 = (a1 + b1)/(2^7) + b1/(2^6) + ... + b1/2 = (a1 + b1)/(2^7) + b1(1/2 + 1/2^2 + ... + 1/2^7))

since 1/2 + 1/2^2 + ... + 1/2^7 is a sum of the first 7 terms of a Geometrical Progression we have

1/2 + 1/2^2 + ... + 1/2^7 = (1/2)(1 - (1/2)^7)/(1 - 1/2) = 127/128 = 128/2^7

m71 = (a1 + b1)/(2^7) + b1*27/(2^7) = (a1 + 28b1)/(2^7)

similar we have

m72 = (a2 + 28b2)/(2^7)

the coordinates of M7 are ( (a1 + 28b1)/(2^7), (a2 + 28b2)/(2^7))

If A(0.0) and B(1,0) that is a1 = a2 = 0 and b1=1, b2 = 0 we have the following solution for M7

M7(28/(2^7), 0) = M7(7/(2^5), 0 )