Solution:

Given line: 3x + 2y – 8 = 0

2y = -3x + 8

y = (-3/2) x + 4

Here, slope (m₁) = -3/2

Now, the co-ordinates of the mid-point of the line segment joining the points (5, -2) and (2, 2) will be

((5 + 2)/7, (-2 + 2)/7) = (7/2, 0)

Let’s consider the slope of the line perpendicular to the given line be m₂

Then,

m₁ x m₂ = -1

(-3/2) x m₂ = -1

m₂ = 2/3

So, the equation of the line with slope m₂ and passing through (7/2, 0) will be

y – 0 = (2/3) (x – 7/2)

3y = 2x – 7

2x – 3y – 7 = 0

Thus, the required line equation is 2x – 3y – 7 = 0.