A) \[x-5y=0\]\[5x+y=0\]\[\Delta =\frac{36}{13}\]
B) \[3x-y=0\]\[x+3y=0\]\[\Delta =\frac{12}{17}\]
C) \[5x-y=0\]\[x+5y=0\]\[\Delta =\frac{13}{5}\]
D) None of these
Correct Answer: A
Solution :
\[y=mx\]. It makes an angle of \[\pm {{45}^{o}}\] with \[2x+3y=6\]. \ \[\tan (\pm {{45}^{o}})=\frac{m-(-2/3)}{1+m(-2/3)}=\pm 1\] or \[3m+2=\pm (3-2m)\]\[\Rightarrow m=\frac{1}{5},-5\] Hence sides are \[x-5y=0,\] \[5x+y=0\] and \[2x+3y=6\]. Solving in pairs, vertices are \[(0,\,0)\], \[\left( \frac{6}{13},\frac{30}{13} \right)\,,\left( \frac{30}{13},-\frac{6}{13} \right)\]. \[\Delta =\left| \frac{1}{2}({{x}_{1}}{{y}_{2}}-{{x}_{2}}{{y}_{1}}) \right|=\frac{1}{2}\times \frac{936}{169}=\frac{36}{13}\].You need to login to perform this action.
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