question_answer

If x\[\left| \begin{matrix}    {{x}_{1}} & {{y}_{1}} & 1  \\    {{x}_{2}} & {{y}_{2}} & 1  \\    {{x}_{3}} & {{y}_{3}} & 1  \\ \end{matrix} \right|=\left| \begin{matrix}    {{a}_{1}} & {{b}_{1}} & 1  \\    {{a}_{2}} & {{b}_{2}} & 1  \\    {{a}_{3}} & {{b}_{3}} & 1  \\ \end{matrix} \right|\]., then the two triangle with vertices \[({{x}_{1}},{{y}_{1}}),\,({{x}_{2}},{{y}_{2}}),\,\] \[({{x}_{3}},{{y}_{3}})\] and \[({{a}_{1}},{{b}_{1}}),\,\]\[\,({{a}_{2}},{{b}_{2}}),\] \[({{a}_{3}},{{b}_{3}})\] must be [IIT 1985]

A) Similar

B) Congruent

C) Never congruent

D) None of these