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10th Class Mathematics Coordinate Geometry Question Bank MCQs - Coordinate Geometry

  • question_answer
    The ratio in which the Line segment joining \[\left( 1,\text{ }-\text{ }5 \right)\] and \[(-4,5)\] is divided by the X-axis is: (ncert exercise)

    A) \[1:1\]

    B) \[1:2\]

    C) \[2:1\]

    D) None of these

    Correct Answer: A

    Solution :

    [a] Let required ratio be \[m & :n\]
    \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,P\equiv \left\{ \frac{m(-4)+n(1)}{m+n},\frac{m(5)+n(-5)}{m+n} \right\}\]
    \[=\left( \frac{-4m+n}{m+n},\frac{5m-5n}{m+n} \right)\]
    Since, that point lies on X-axis
    \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\frac{5m-5n}{m+n}=0\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,5m-5n=0\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,m:n=1:1\]


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