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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 (0, 0), \[(2,\,2\sqrt{3})\] and (a, b) be the vertices of an equilateral triangle, then \[(a,\,b)=\]

    A) (0, - 4)

    B) (0, 4)

    C) (4, 0)

    D) (- 4, 0)

    Correct Answer: C

    Solution :

    \[l=\sqrt{4+12}=4\,\,\Rightarrow \,\,{{a}^{2}}+{{b}^{2}}=16\] and \[{{(a-2)}^{2}}+{{(b-2\sqrt{3})}^{2}}=16\,\,\Rightarrow \,\,a+\sqrt{3}b=4\] Hence\[(a,\,\,b)=(4,\,\,0)\].


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