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JEE Main & Advanced Mathematics Straight Line Question Bank Distance between two lines, Perpendicular distance of the line from a point Position of point w.r.t. line

  • question_answer
    The distance of the point of intersection of the lines \[2x-3y+5=0\] and \[3x+4y=0\]from the line \[5x-2y=0\] is

    A)            \[\frac{130}{17\sqrt{29}}\]

    B)            \[\frac{13}{7\sqrt{29}}\]

    C)            \[\frac{130}{17}\]                   

    D)            None of these

    Correct Answer: A

    Solution :

               Points of intersection are \[y=\frac{15}{17},x=\frac{-4\times 15}{3\times 17}=\frac{-20}{17}\]                    Therefore\[D=\left| \frac{5\left( \frac{-20}{17} \right)-2\left( \frac{15}{17} \right)}{\sqrt{29}} \right|=\frac{130}{17.\sqrt{29}}\].


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