Question

The area of the triangle, formed by the straight lines $7x-2y+10=0$, $7x+2y-10=0$ forms an issosceles triangle with the line $y=2$, is

• A. $\frac{686}{275}$
• B. $\frac{18}{7}$
• C. $\frac{686}{276}$
• D. $Noneofthese$

Answer 1

The correct option is B $\frac{18}{7}$

$7x-2y+10=0\Rightarrow 7x-2y=-10\Rightarrow \frac{x}{-\frac{10}{7}}+\frac{y}{5}=1$

$7x+2y-10=0\Rightarrow 7x+2y=10\Rightarrow \frac{x}{\frac{10}{7}}+\frac{y}{5}=1$

$7x-2y+10=0,y=27x-4+10=0\Rightarrow x=\frac{-6}{7}$

$7x+2y-10=0,y=27x+4-10=0\Rightarrow x=\frac{6}{7}$

The coordinates of P & Q are $(\frac{-6}{7},2)$ & $(\frac{6}{7},2)$ respectively.

$\therefore$ The area of the triangle $=\left|\begin{array}{ccc}0& 5& 1\\ \frac{-6}{7}& 2& 1\\ \frac{6}{7}& 2& 1\end{array}\right|=\frac{6}{7}\left|\begin{array}{ccc}0& 5& 1\\ -1& 2& 1\\ 1& 2& 1\end{array}\right|=\frac{6}{7}.0-\frac{6}{7}.5(-1-1)+1.(-2-2)=\frac{60}{7}-4=\frac{32}{7}squnits$