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Question: \(P(2,1),Q(4, - 1),R(3,2)\) are the vertices of triangle and if through P and R lines parallel to op...

P(2,1),Q(4,−1),R(3,2)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

Answer

4

Explanation

Solution

Since PQRS is a parallelogram with an area which is twice the area of △PQR\triangle P Q R.

Therefore, area PQRS

=2⋅12∣2114−11321∣=4= 2 \cdot \frac { 1 } { 2 } \left| \begin{array} { c c c } 2 & 1 & 1 \\ 4 & - 1 & 1 \\ 3 & 2 & 1 \end{array} \right| = 4.