In each of the following find the value of ‘k’, for which the points are collinear
(7, –2), (5, 1), (3, k)

Let the given points be A(7, -2), B(5, 1) and C(3, K)
Here, we have,
x₁ = 7, y₁ = -2
x₂ = 5, y₂ = 1
and    x₃ = 3, y₃ = K
Now, Area of ∆ABC

If the points are collinear, then area of the triangle = 0
⇒    4 - k = 0
⇒    k = 4.