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JEE Main & Advanced Mathematics Rectangular Cartesian Coordinates Question Bank System of co-ordinates, Distance between two points, Section formulae

  • question_answer
    The extremities of a diagonal of a parallelogram are the points \[(3,-4)\]and \[(-6,5)\]. If third vertex is \[(-2,1)\], then fourth vertex is [RPET 1987]

    A) \[(1,0)\]

    B) \[(-1,0)\]

    C) \[(1,\text{ }1)\]

    D) None of these

    Correct Answer: B

    Solution :

    Let A (3, - 4) and C(- 6, 5) be the ends of diagonal of parallelogram ABCD. Let B (- 2, 1) and D be (x, y). Then mid-points of diagonals AC and BD coincide. So \[\frac{x-2}{2}=\frac{-6+3}{2}\] and \[\frac{y+1}{2}=\frac{5-4}{2}\,\,\Rightarrow \,\,x=-1,\,\,y=0\] \[\therefore \] Coordinates of D are (-1, 0).


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