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JEE Main & Advanced JEE Main Solved Paper-2016

  • question_answer
    Two sides of a rhombus are along the lines, \[x-v+1=0\]and \[\text{7x}\text{y}\text{5}=0.\] If its diagonals intersect at (-1, -2), then which one of the following is a vertex of this rhombus ? [JEE Main Solved Paper-2016 ]

    A) \[\left( -\frac{10}{3},\frac{7}{3} \right)\]                               

    B) \[(-3,-9)\]

    C) \[(-3,-8)\]                           

    D) \[\left( \frac{1}{3},\frac{8}{3} \right)\]

    Correct Answer: D

    Solution :

                    Equation of angle bisector of the lines  \[\text{x}\text{y}+\text{1}=0\]and \[\text{7x}\text{y}\text{5}=0\] is given by \[\frac{x-y+1}{\sqrt{2}}=\pm \frac{7x-y-5}{5\sqrt{2}}\] \[\Rightarrow \]\[5(x-y+1)=7x-y-5\] \[\therefore \]\[2x+4y-10=0\Rightarrow x+2y-5=0\]and Now equation of diagonals are \[(x+1)+2y(y+2)=0\Rightarrow x+2y+5=0\]          ..(1) and\[2(x+1)-(y+2)=0\Rightarrow 2x-y=0\]            ...(2) Clearly\[\left( \frac{1}{3},\frac{8}{3} \right)\]lies on (1)


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