Question

Question:
Hindi
If the points (1,1 (2,3), (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 (2,3) = slope of (1, 1) and (5, k)

⇒ (3 - 1)/(2 - 1) = (k - 1)/(5 - 1)

⇒ 2/1 = (k - 1)/4

⇒ 8 = 1(k - 1)

⇒ 8 + 1 = k

⇒ 9 = k

       Method 2:

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

 Slope of line =  (3 - 1)/(2 - 1) = 2

Therefore, equation of line is:

⇒ (y - y₁) = m(x - x₁)

⇒ y - 1 = 2(x - 1)

⇒ 2x - y - 1 = 0  

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

⇒ 2(5) - k - 1 = 0

⇒ 10 - 1 = k

⇒ 9 = k