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JEE Main & Advanced Mathematics Straight Line Question Bank Foot of perpendicular, Transformation, Pedal points Image of a point

  • question_answer
    The coordinates of the foot of the perpendicular from the point (2, 3) on the line \[y=3x+4\] are given by [MP PET 1984]

    A)            \[\left( \frac{37}{10},-\frac{1}{10} \right)\]                               

    B)            \[\left( -\frac{1}{10},\frac{37}{10} \right)\]

    C)            \[\left( \frac{10}{37},-10 \right)\]   

    D)            \[\left( \frac{2}{3},-\frac{1}{3} \right)\]

    Correct Answer: B

    Solution :

               \[-y+3x+4=0\]and perpendicular is \[\frac{y-3}{x-2}=\frac{-1}{3}\] or \[3y+x-11=0\]. Therefore foot is \[x=\frac{-1}{10},y=\frac{37}{10}\].


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