STD 11 - rectangular cartensian co-ordinates — Maths STD 11 Science — Question

ase said to be cerlineas if Area $(\Delta A B C)=0$

$=\frac{S}{2}\left|\begin{array}{lll}2 & y & 1 \\ x_{2} & y_{2} & 1 \\ x_{3} & y_{3} & 1\end{array}\right|=0$

$\therefore \quad\left|\begin{array}{lll}\lambda+1 & 1 & 1 \\ 2 \lambda+1 & 3 & 1 \\ 2 \lambda+2 & 2 \lambda & 1\end{array}\right|=0$

$\Rightarrow(\dot{x}+1)(3-2 \lambda)-1(82+1-2 \lambda-2)$

$+1\left(4 x^{2}+2 x-6 x-6\right)=0$

$\Rightarrow 3 \lambda+3-2\left(\lambda^{2}-2 \lambda+1+4 x^{2}-4 \lambda-6=0\right.$

$\Rightarrow 2 \lambda^{2}-3 \lambda-2=0$

$\Rightarrow 2 \lambda^{2}-4 \lambda+\lambda-2=0$

a) $2 x(x-2)+1(x-2)=0$

$\Rightarrow \lambda=-1 / 2$ or 2

" polsible values of

$\lambda \operatorname{are} 2$