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10th Class Mathematics Coordinate Geometry Question Bank MCQs - Coordinate Geometry

  • question_answer
    If three points (0, 0), \[\left( 3,\,\sqrt{3} \right)\]and \[\left( 3,\,\lambda  \right)\]form an equilateral triangle, then \[\lambda \], equals

    A) 2

    B) -3

    C) -4

    D) None of these

    Correct Answer: D

    Solution :

    Let the given points are A (0,0), \[B\left( 3,\,\sqrt{3} \right)\]and \[C\left( 3,\,\lambda  \right)\].
    Since, \[\Delta ABC\]is an equilateral triangle,
    Therefore
                                        AB=AC
    \[\Rightarrow \,\,\,\sqrt{{{\left( 3-0 \right)}^{2}}+{{\left( \sqrt{3}-0 \right)}^{2}}}=\sqrt{{{\left( 3-0 \right)}^{2}}+{{\left( \lambda -0 \right)}^{2}}}\]
    \[\Rightarrow \,\,\,9+3=9+{{\lambda }^{2}}\]
    \[\Rightarrow \,\,\,{{\lambda }^{2}}=3\]
    \[\Rightarrow \,\,\,\,\lambda =\pm \sqrt{3}\]
     


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