JEE Main & Advanced Mathematics Straight Line Question Bank Critical Thinking

  • question_answer The sides \[AB,BC,CD\] and \[DA\]of a quadrilateral are \[x+2y=3,\,x=1,\] \[x-3y=4,\,\] \[\,5x+y+12=0\] respectively.  The angle between diagonals \[AC\]and \[BD\]is  [Roorkee 1993]

    A)            \[{{45}^{o}}\]                            

    B)            \[{{60}^{o}}\]

    C)            \[{{90}^{o}}\]                            

    D)            \[{{30}^{o}}\]

    Correct Answer: C

    Solution :

               The four vertices on solving are \[A(-3,\,3)\], \[B(1,\,1),\] \[C(1,\,-1)\] and \[D(-2,-2)\].\[{{m}_{1}}\]= slope of \[AC=-1\], \[{{m}_{2}}\]= slope of \[BD=1\]; \\[{{m}_{1}}{{m}_{2}}=-1\].                    Hence the angle between diagonals AC and BD is \[90{}^\circ \].

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