As (a, b) is the mid-point of the line segment A(10, -6) and B(k, 4)
So,
(a, b) = (10 + k / 2, -6 + 4/ 2)
a = (10 + k)/ 2 and b = -1
2a = 10 + k
k = 2a – 10
Given, a – 2b = 18
Using b = -1 in the above relation we get,
a – 2(-1) = 18
a = 18 – 2 = 16
So,
k = 2(16) – 10 = 32 – 10 = 22
Thus,
AB = √[(22 – 10)2 + (4 + 6)2]
= √[(12)2 + (10)2]
= √[144 + 100]
= 2√61 units