Question

Find the value of ‘k’ for which the points (3k – 1, k – 2), (k, k – 7) and (k – 1, -k -2) are collinear.

Answer 1

Given points are collinear 

Let A (3k – 1, k – 2), B (k, k – 7) and 

C (k – 1, -k – 2) are on the same line \(\overleftrightarrow{LN}\)

Then slope of \(\overline{AB}\) and slope of \(\overline{AC}\) should be same (∵ they are collinear)

Formula for slope

Now (1) = (2)

⇒ \(\frac{-5}{1-2k}\) = 1

⇒ 1 – 2k = -5 

⇒ 1 + 5 = 2k 

⇒ 2k = 6 

∴ k = 3