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JEE Main & Advanced Mathematics Rectangular Cartesian Coordinates Question Bank Critical Thinking

  • question_answer
    If coordinates of the points A and B are (2, 4) and (4, 2) respectively and point M is such that A-M-B also AB = 3 AM, then the coordinates of M are

    A) \[\left( \frac{8}{3},\,\frac{10}{3} \right)\]

    B) \[\left( \frac{10}{3},\frac{14}{4} \right)\]

    C) \[\left( \frac{10}{3},\frac{6}{3} \right)\]

    D) \[\left( \frac{13}{4},\frac{10}{4} \right)\]

    Correct Answer: A

    Solution :

    Since \[AB=3AM\,\,\] \[\Rightarrow \,\,AM+MB=3AM\,\,\Rightarrow \,\,MB=2AM\] Hence ratio \[AM\,\,:\,\,MB=1\,\,:\,\,2\] Therefore the point \[M\,\left( \frac{8}{3},\,\,\frac{10}{3} \right)\].


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