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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
    If \[A(3,\,5),B(-5,\,-4),C(7,\,10)\] are the vertices of a parallelogram, taken in the order, then the co-ordinates of the fourth vertex are [Kerala (Engg.) 2005]

    A) (10, 19)

    B) (15, 10)

    C) (19, 10)

    D) (19, 15)

    E) (e) (15, 19)

    Correct Answer: E

    Solution :

    (e) Mid point of \[A(3,5)\] and \[C(7,10)\]= \[M\left( 5,\,\,\frac{15}{2} \right)\] \ Mid point of \[BD=M\left( 5,\,\,\frac{15}{2} \right)\] \[B(-5,-4)\] and \[D(x,y)\] \ \[\frac{-5+x}{2}=5\];  \[x=10+5=15\] \[\frac{-4+y}{2}=\frac{15}{2}\];  \[y=15+4=19\] Co-ordinates of fourth vertex \[D=(15,\ 19)\].


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