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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 point which divides externally the line joining the points \[(a+b,\,a-b)\] and \[(a-b,a+b)\] in the ratio \[a:b\], is

    A) \[\left( \frac{{{a}^{2}}-2ab-{{b}^{2}}}{a-b},\frac{{{a}^{2}}+{{b}^{2}}}{a-b} \right)\]

    B) \[\left( \frac{{{a}^{2}}-2ab-{{b}^{2}}}{a-b},\frac{{{a}^{2}}-{{b}^{2}}}{a-b} \right)\]

    C) \[\left( \frac{{{a}^{2}}-2ab+{{b}^{2}}}{a-b},\frac{{{a}^{2}}+{{b}^{2}}}{a-b} \right)\]

    D) None of these

    Correct Answer: A

    Solution :

      Here \[x=\frac{a\,(a-b)-b\,(a+b)}{a-b}=\frac{{{a}^{2}}-2ab-{{b}^{2}}}{a-b}\] \[y=\frac{a\,(a+b)-b\,(a-b)}{a-b}=\frac{{{a}^{2}}+{{b}^{2}}}{a-b}\].


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