Question

if the point (1,1), (2,2), (5,k) are collinear then the value of k is​

Answer 1

If they are collinear they must have same slope(or you can say, they lie on the same line).

Slope of (1,1) and (2,2) = slope of (1, 1) and (5, k)

⇒ (2 - 1)/(2 - 1) = (k - 1)/(5 - 1)

⇒ 1/1 = (k - 1)/4

⇒ 4 = 1(k - 1)

⇒ 4 + 1 = k

⇒ 5 = k

       Method 2:

As they lie on the same line, they must satisfy the equation of line.

 Slope of line =  (2 - 1)/(2 - 1) = 1

Therefore, equation of line is:

⇒ (y - y₁) = 1(x - x₁)

⇒ y - 1 = 1(x - 1)

⇒ x - y = 0  

    As this defines the whole line, it must satisfy (x , y) = (5, k)

⇒ (5) - k = 0

⇒ 5 = k