Here, given points are P (2, 1) and Q (5, - 8) which is trisected at the points(say) A(x₁ , y₁) and B(x₂ , y₂)such that A is nearer to P.

By section formula,

x = , y =

For point A(x₁ , y₁) of PQ, where m = 1 and n = 2,

x₁ = , y₁ =

∴ x₁ = 3 , y₁ = -2

∴Coordinates of A is (3,-2)

It is given that point A lies on the line 2x - y + k = 0.

So, substituting value of x and y as coordinates of A,

2 × 3 – (-2) + k = 0

∴ k = -8