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JEE Main & Advanced Mathematics Straight Line Question Bank Critical Thinking

  • question_answer
    The line \[3x+2y=24\]meets \[y\]-axis at A and x-axis at B. The perpendicular bisector of \[AB\]meets the line through \[(0,-1)\] parallel to x-axis at C. The area of the triangle \[ABC\] is 

    A)            \[182sq.\]units                         

    B)            \[91sq.\]units

    C)            \[48sq.\]units                           

    D)            None of these

    Correct Answer: B

    Solution :

               The coordinates of A and B are \[(0,\,12)\]and \[(8,0)\] respectively. The equation of the perpendicular bisector of AB is \[y-6=\frac{2}{3}(x-4)\] or \[2x-3y+10=0\] .....(i)                    Equation of a line passing through (0, ?1) and parallel to x-axis is \[y=-1\]. This meets (i) at C, Therefore the coordinates of C are\[\left( -\frac{13}{2},-1 \right)\].                    Hence the area of the triangle \[ABC\]is                    \[\Delta =\frac{1}{2}\left| \begin{matrix}    0 & 12 & 1  \\    8 & 0 & 1  \\    -\frac{13}{2} & -1 & 1  \\ \end{matrix}\, \right|=91\] sq. units.


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