JEE Main & Advanced Mathematics Straight Line Question Bank Problems related to triangle and quadrilateral Locus

  • question_answer
    The triangle formed by the lines \[x+y-4=0,\,\] \[3x+y=4,\] \[x+3y=4\] is            [RPET 2002; IIT 1983; MNR 1992; UPSEAT 2001]

    A)            Isosceles                                   

    B)            Equilateral

    C)            Right?angled                            

    D)            None of these

    Correct Answer: A

    Solution :

               The vertices of triangle are the intersection points of these given lines. The vertices of \[\Delta \] are \[A(0,\,4),\] \[B(1,2),\]\[C(4,0)\]            Now,           \[AB=\sqrt{{{(0-1)}^{2}}+{{(4-1)}^{2}}}=\sqrt{10}\]                                 \[BC=\sqrt{{{(1-4)}^{2}}+{{(0-1)}^{2}}}=\sqrt{10}\]                                 \[AC=\sqrt{{{(0-4)}^{2}}+{{(0-4)}^{{}}}}=4\sqrt{2}\]                    \[\because AB=BC\]; \ D is isosceles.


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