Question

Three points $(p + 1,\ 1)$, $(2p + 1,\ 3$) and $(2p + 2,\mspace{6mu} 2p)$ are collinear, if p =

• A. – 1
• B. 1
• C. 2
• D. 0

Answer 1

Answer: (C)

2

Answer 2

$\left| \begin{array} { c c c } p + 1 & 1 & 1 \\ 2 p + 1 & 3 & 1 \\ 2 p + 2 & 2 p & 1 \end{array} \right| = 0$

$\Rightarrow ( p + 1 ) ( 3 - 2 p ) + 1 ( 2 p + 2 - 2 p - 1 )$ $+ 1 [ ( 2 p ) ( 2 p + 1 ) - 3 ( 2 p + 2 ) ] = 0$

$\Rightarrow p = 2$.