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JEE Main & Advanced Mathematics Rectangular Cartesian Coordinates Question Bank Points related to triangle (Orthocente Circumcentre Incentre), Area of some geometrical figures Collinearity

  • question_answer
    Three points \[(p+1,\text{ }1)\], \[(2p+1,\text{ }3\]) and \[(2p+2,\ 2p)\] are collinear, if p =  [MP PET 1986]

    A) - 1

    B) 1

    C) 2

    D) 0

    Correct Answer: C

    Solution :

    \[\left| \,\begin{matrix}    p+1 & 1 & 1  \\    2p+1 & 3 & 1  \\    2p+2 & 2p & 1  \\ \end{matrix}\, \right|=0\] \[\Rightarrow \,\,(p+1)\,(3-2p)+1(2p+2-2p-1)\]\[+1\,[(2p)\,(2p+1)-3\,(2p+2)]=0\] \[\Rightarrow \,\,p=2\].


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