Given points are A(8,1),B(3,−4) and C(2,k).It is also said that they are collinear and hence 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 ∆ABC = 0

∴ 0 = |8(-4 – k) + 3(k – 1) + 2(1 – (-4))|

∴ 0 = |-32 – 8k + 3k -3 + 10|

∴ 5k + 25 = 0

∴ k = -5

Hence, the value of k is -5.