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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 with vertices \[\left( 2,\,\frac{\sqrt{3}-1}{2} \right)\], \[\left( \frac{1}{2},\,-\frac{1}{2} \right)\] and \[\left( 2,\,-\frac{1}{2} \right)\] is   [IIT 1993]

    A) \[\left( \frac{3}{2},\,\frac{\sqrt{3}-3}{6} \right)\]

    B) \[\left( 2,\,-\frac{1}{2} \right)\]

    C) \[\left( \frac{5}{4},\,\frac{\sqrt{3}-2}{4} \right)\]

    D) \[\left( \frac{1}{2},\,-\frac{1}{2} \right)\]

    Correct Answer: B

    Solution :

    Here, the given triangle is a right angled triangle at the vertex \[\left( 2,-\frac{1}{2} \right)\]. Hence the orthocentre is at \[\left( 2,\frac{-1}{2} \right)\].


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