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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 orthocentre of the triangle formed by the lines \[x+y=1,\,2x+3y=6\] and \[4x-y+4=0\] lies in quadrant  [IIT 1985]

    A) First

    B) Second

    C) Third

    D) Fourth

    Correct Answer: A

    Solution :

    On solving the equations, we get the two vertices (-3, 4) and \[\left( \frac{-3}{7},\frac{16}{7} \right)\]. Also perpendicular passes through vertices are \[x+4y=13\] and \[7x-7y=-19\]. Solving these lines, we get the orthocentre \[\left( \frac{3}{7},\frac{22}{7} \right)\] i.e. in first quadrant.


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