Mathematics - Point Question with Solution | TestHub

If $P, Q, R$ are mid-points of sides of $∆ABC$ then  $4\times Area\left(\mathrm{\Delta PQR}\right)=Area(∆\mathrm{ABC})$

Area of $\Delta \mathrm{ABC}=4\times \frac{1}{2}\left|\frac{{\left|\begin{array}{lll}{\mathrm{a}}_1& { \mathrm{b}}_1& {\mathrm{c}}_1\\ {\mathrm{a}}_2& { \mathrm{b}}_2& {\mathrm{c}}_2\\ {\mathrm{a}}_3& { \mathrm{b}}_3& {\mathrm{c}}_3\end{array}\right|}^2}{{\mathrm{C}}_1{\mathrm{C}}_2{\mathrm{C}}_3}\right|$ 

Where ${\mathrm{C}}_1,{\mathrm{C}}_2,{\mathrm{C}}_3$ are cofactors of$c_1,c_2,c_3$

$\Delta \mathrm{ABC}=4\times \frac{1}{2}\left|\frac{{\left|\begin{array}{lll}1& -1& 1\\ 1& -2& 3\\ 2& -5& 11\end{array}\right|}^2}{(-1)\left(3\right)(-1)}\right|$

$=2\times 9÷3$

$=6$