Question

If (a, b), (c, d) and (a - c, b - d) are collinear, then which one of the following is correct ?

• A. bc - ad = 0
• B. ab - cd = 0
• C. bc + ad = 0
• D. ab + cd = 0

Answer 1

Answer: (A)

bc - ad = 0

Answer 2

Let A, B and C having co-ordinates (a, b), (c, d) and {(a - c), (b - d)} respectively be the points If these poins are collinear then $\begin{vmatrix}a&b&1\\\ c&d&1\\\ a-c&b-d&1\end{vmatrix} = 0$ On solving this expression we get 1. {a (d - b) - b (c - a)}= 0 $\Rightarrow$ ad - ab - bc + ab = 0 $\Rightarrow$ bc - ad = 0