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JEE Main & Advanced Mathematics Rectangular Cartesian Coordinates Question Bank System of co-ordinates, Distance between two points, Section formulae

  • question_answer
    If the points \[A(6,-1),\ B\text{ }(1,\,3)\] and \[C(x,\,8)\]be such that \[AB=BC,\]then  \[x=\]

    A) - 3, 5

    B) 3, - 5

    C) - 3, - 5

    D) 3, 5

    Correct Answer: A

    Solution :

    \[AB=BC\,\,\Rightarrow \,\,{{(6-1)}^{2}}+{{(3+1)}^{2}}={{(x-1)}^{2}}+{{(8-3)}^{2}}\] \[\Rightarrow \,\,{{(x-1)}^{2}}-{{(4)}^{2}}=0\,\,\Rightarrow \,\,x=5,\,\,-\,3\].


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