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JEE Main & Advanced Mathematics Rectangular Cartesian Coordinates Question Bank Points related to triangle (Orthocente Circumcentre Incentre), Area of some geometrical figures Collinearity

  • question_answer
    If \[A(6,3),\]\[B(-3,5)\], \[C(4,-2)\] and \[D(x,\text{ }3x)\]are four points. If the ratio of area of \[\Delta DBC\]and \[\Delta ABC\]is 1 : 2, then the value of x, will be [IIT 1959]

    A) \[\frac{11}{8}\]

    B) \[\frac{8}{11}\]

    C) \[3\]

    D) None of these

    Correct Answer: A

    Solution :

    \[\frac{\Delta \,DBC}{\Delta \,ABC}=\frac{1}{2}\Rightarrow \,\,2\Delta DBC=\Delta ABC\] \[\Rightarrow \,\,2(14x-7)=\frac{49}{2}\,\,\Rightarrow \,\,x=\frac{77}{56}=\frac{11}{8}\].


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