If the point P (2, 1) lies on the line segment joining points A (4, 2) and B (8, 4), then

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 (x_{1}, y_{1}) and (x_{2}, y_{2}),

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 =

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