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SSC Quantitative Aptitude Coordinate Geometry Question Bank Coordinate Geometry and Graphs of Linear Equations (II)

  • question_answer
    If the points\[(1,1),\,(-1,-1),\]\[(-\,\sqrt{3},\sqrt{3})\]are the vertices of a triangle, then this triangle is

    A) right angled

    B) isosceles

    C) equilateral

    D) None of the above

    Correct Answer: C

    Solution :

    [c] Let \[P\,(1,\,1),Q\,(-1,\,-1)\]and \[R\,(-\,\sqrt{3},\,\sqrt{3})\]are vertices of \[\Delta PQR.\] \[\therefore \]      \[PQ=\sqrt{{{(1+1)}^{2}}+{{(1+1)}^{2}}}=\sqrt{8}=2\sqrt{2}\] \[QR=\sqrt{{{(-2\sqrt{3}-1)}^{2}}+{{(\sqrt{3}+1)}^{2}}}=\sqrt{8}=2\sqrt{2}\]Similarly, \[PR=\sqrt{{{(-\,\sqrt{3}-1)}^{2}}+{{(\sqrt{3}-1)}^{2}}}=\sqrt{8}=2\sqrt{2}\]\[\therefore \]        \[PQ=QR=PR\] Which shows \[\Delta PQR\] is an equilateral.


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