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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 are \[A(6,\text{ }3),\,B\text{ }(-\,3,\text{ }5),\,C\text{ }(4,\text{ }-2)\]and P (x, y) is a point, then the ratio of area of \[\Delta \]PBC and \[\Delta \]ABC is       [IIT 1983]

    A) \[\left| \frac{x+y-2}{7} \right|\]

    B) \[\left| \frac{x-y+2}{2} \right|\]

    C)   \[\left| \frac{x-y-2}{7} \right|\]

    D) None of these

    Correct Answer: A

    Solution :

    \[\frac{\Delta \,PBC}{\Delta \,ABC}=\left| \frac{[-3(-2-y)+4(y-5)+x(5+2)]}{[6\,(5+2)-3(-2-3)+4(3-5)]} \right|\]                               \[=\left| \frac{7x+7y-14}{49} \right|=\left| \frac{x+y-2}{7} \right|\].


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