To find the minimum distance from the origin (0,0) to a point on the line segment connecting points A(3, 0) and B(0, 4), we will use the concept of perpendicular distances in coordinate geometry.

The formula to find the shortest distance from a point to a line is derived from the line equation. First, let's determine the equation of the line segment AB:

1. Calculate the slope of the line segment AB: \(\text{Slope of AB} = \frac{4-0}{0-3} = -\frac{4}{3}\).
2. Using the point-slope form of a line, \(y-y_1=m(x-x_1)\), choose point A(3,0): \(y - 0 = -\frac{4}{3}(x - 3)\).
3. Simplify to get the standard form: \(4x + 3y = 12\).

The equation of the line is \(4x + 3y = 12\).

Next, find the perpendicular distance from the origin (0,0) to the line:

1. Use the formula for the distance from a point \((x_1, y_1)\) to the line \(Ax + By + C = 0\): \(\text{Distance} = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}\).
2. Substitute \(A = 4, B = 3, C = -12, x_1 = 0, y_1 = 0\): \(\text{Distance} = \frac{|4 \cdot 0 + 3 \cdot 0 - 12|}{\sqrt{4^2 + 3^2}} = \frac{|-12|}{\sqrt{16 + 9}} = \frac{12}{5} = 2.4\).

Therefore, the minimum distance from the origin to the line segment AB is 2.4.

This distance can be achieved when a perpendicular is drawn from the origin to the line AB since it falls on the line segment AB itself. Thus, the correct answer is 2.4.