11th Class
Mathematics
Sample Paper
Mathematics Olympiad - Sample Paper-6
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.