Since, the points

A = (5, 1)

B = ( - 2 – 3)

C = (8, 2m) are collinear

Area of ∆ABC = 0

1/2 [x₁ (y₂ - y₃ ) + x₂ (y₃ - y₁ ) + x₃ (y₁ - y₂ )]=0

1/2 [5( - 3 - 2m) + ( - 2)(2m - 1) + 8(1 - ( - 3))]=0

1/2 ( - 15 – 10m – 4m + 2 + 32) = 0

1/2 ( - 14m + 19) = 0

m = 19/14

Hence, the value of m =