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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 (0, 0), (8, 0), (4 6) is    [EAMCET 1991]

    A) \[\left( 4,\,\frac{8}{3} \right)\]

    B) (3, 4)

    C) (4, 3)

    D) (-3, 4)

    Correct Answer: A

    Solution :

    Let the vertices of the triangle be O(0, 0) \[A(8,0),\] \[B(4,6)\]. The equation of an altitude through O and perpendicular to AB is \[y=\frac{2}{3}x\]and the equation of an altitude through \[A(8,0)\] and perpendicular to OB is  \[3y=-2x+16\]. The two altitudes intersect at \[\left( 4,\frac{8}{3} \right)\].


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