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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
    The vertices of the triangle ABC are (2,1), (4,3) and (2,5). \[D,\,E,\,F\]are the mid-points of the sides. The area of the triangle DEF  is   

    A) 1

    B) 1.5

    C) 3

    D) 4

    Correct Answer: A

    Solution :

    \[D\,\,(3,\,\,2),\,\,E\,(3,\,\,4),\,\,F\,(2,\,\,3)\] Area\[=\frac{1}{2}\,\left| \,\begin{matrix}    3 & 2 & 1  \\    3 & 4 & 1  \\    2 & 3 & 1  \\ \end{matrix}\, \right|\]\[=\frac{1}{2}[3\,(4-3)-2(3-2)+1(9-8)]\]        = 1 sq. units.


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