It is said that the point P(m,3) lies on the line segment joining the points A( and B (2, 8).

Hence we understand that these three points are collinear. So the area enclosed by them should be 0.

Area of the triangle having vertices (x₁,y₁), (x₂,y₂) and (x₃,y₃)

= |x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)|

Given that area of ∆ABP = 0

∴ 0 = |m(6 – 8) - (8 – 3) + 2(3 – 6)|

∴ -2m – 2 -6 = 0

-2m = 8

m = -4

Hence the value of m = -4