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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2000

  • question_answer
    If\[x>0\]and\[A=(-3,4),B=(-1,-2),\]\[C=(5,6),D=(x,-4)\]are the vertices of a quadrilateral such that \[\Delta ABD=2\Delta ACD,\]then the value of\[x\]is:

    A)  6                            

    B)                         9                            

    C)         69                                         

    D)         96

    E)         3

    Correct Answer: C

    Solution :

    Area of \[\Delta ABD=2\Delta ACD\] \[\Rightarrow \] \[\frac{1}{2}\left| \begin{matrix}    -3 & 4 & 1  \\    -1 & -2 & 1  \\    x & -4 & 1  \\ \end{matrix} \right|=2\times \frac{1}{2}\left| \begin{matrix}    -3 & 4 & 1  \\    5 & 6 & 1  \\    x & -4 & 1  \\ \end{matrix} \right|\] \[\Rightarrow \] \[\left| \begin{matrix}    -3 & 4 & 1  \\    2 & -6 & 0  \\    x+3 & -8 & 0  \\ \end{matrix} \right|=2\left| \begin{matrix}    -3 & 4 & 1  \\    8 & 2 & 0  \\    x+3 & -8 & 0  \\ \end{matrix} \right|\] \[\Rightarrow \] \[-16+6x+18=2(-64-2x-6)\] \[\Rightarrow \] \[6x+2=|-2(2x+70)|\Rightarrow x=69\]


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