Given,

Point P (2, 1) lies on the line segment AB, joining the points A (4, 2) and B (8, 4);

Now,

The distance between A (4, 2) and P (2, 1),

By using the distance formula;

∵ Distance between two points (x₁, y₁) and (x₂, y₂),

d =

AP =

Distance between A (4, 2) and B (8, 4)

AB

Distance between B (8, 4) and P (2, 1),

BP =

∴ AB =

2AP = AB

Hence, required condition is AP =