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  • A pair of straight lines drawn through the origin forms with line <img alt="\mathrm{2x + 2y = 6}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B2x%20&plus;%202y%20%3D%206%7D"

A pair of straight lines drawn through the origin forms with line \mathrm{2x + 2y = 6} an isosceles right angled triangle, then the area of the triangle thus formed is

Option: 1

\frac{13}{5}


Option: 2

\frac{12}{17}


Option: 3

\frac{36}{13}


Option: 4

\frac{9}{2}


Answers (1)

The line \mathrm{2 x+2 y=6} can be written as \mathrm{\frac{x}{3}+\frac{y}{3}=1}

Therefore, the triangle is \mathrm{ O A B} where \mathrm{A\: is \: (3,0)\: and \: B \: is \: (0,3).}

Thus, the area of \mathrm{\triangle O A B} is

\mathrm{ \frac{1}{2}(O A)(O B) }

\mathrm{= \frac{1}{2}(3)(3)=\frac{9}{2} }.

Hence option 4 is correct.
 

Posted by

Sumit Saini

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