Given that point C(k, 4) divides the join of A(2, 6) and B(5, 1) in the ratio 2 : 3.

∴ m:n = 2:3

Recall that if (x,y) ≡ (a,b) then x = a and y = b

Let (x,y) ≡ (k,4)

(x₁,y₁) ≡ (2,6)

and, (x₂,y₂) ≡ (5,1)

Now, Using Section Formula-

On dividing numerator and denominator of R.H.S by n, we get-

∴ k = (16/5)

Thus the value of k is (16/5).