question_answer

The three points \[\mathbf{A}\left( \mathbf{a},-\mathbf{1} \right),\mathbf{B}\left( \mathbf{2},\mathbf{1} \right)\]and \[\mathbf{C}\left( \mathbf{4},\mathbf{5} \right)\]are collinear points then value of a is:

A)  \[a=2\]                        

B)  \[a=3\]           

C)  \[a=1\]                        

D)  \[a=0\]

Correct Answer: C

Solution :

[c] \[\because A,B,C\]be collinear, then \[\Delta ABC=0\] \[-12+4\left( 4-a \right)=0\] \[4-a=\frac{12}{4}=3\] \[a=4-3=1\] Hence, option [c] is correct.