question_answer

\[P(2,1),\,Q(4,-1),\,R(3,2)\] are the vertices of triangle and if through P and R lines parallel to opposite sides are drawn to intersect in S, then the area of PQRS is

A) 6

B) 4

C) 8

D) 12

Correct Answer: B

Solution :

Since PQRS is a parallelogram with an area which is twice the area of \[\Delta PQR\]. Therefore, area PQRS \[=2.\frac{1}{2}\,\left| \,\begin{matrix}    2 & 1 & 1  \\    4 & -1 & 1  \\    3 & 2 & 1  \\ \end{matrix}\, \right|=4\].