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A = (s, 2s), B = (3s, 8s)

The midpoint of AB is C = [(s + 3s)/2, (2s + 8s)/2] = [4s/2, 10s/2] = (2s, 5s)

Gradient of AB = (8s - 2s)/(3s - s) = 6s/2s = 3

Gradient of perpendicular to AB = -1/(slope AB) = -1/3

Now,

line through C = (2s, 5s) with gradient -1/3 is

y - 5s = -1/3*(x - 2s) = 1/3*(2s - x)

or 3y - 15s = 2s - x

or x + 3y = 17s

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Q: How do you determine the equation for the perpendicular bisector of the straight line joining the points s 2s and 3s 8s?

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