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10th Class Mathematics Coordinate Geometry Question Bank Coordinate Geometry

  • question_answer
    Find the coordinates of the point on X-axis which are equidistant from the points \[(-3,4)\] and (2, 5).

    A)  \[(20,0)\]       

    B)  \[(-23,0)\]       

    C)  \[\left( \frac{4}{7},0 \right)\]       

    D)  None of these 

    Correct Answer: C

    Solution :

    Let \[P(x,0)\] be the point on x-axis which is equidistant from points \[A(-3,4)\] and \[B\,(2,5)\] Distance AP = Distance BP \[\sqrt{{{(x+3)}^{2}}+{{(0-4)}^{2}}}=\sqrt{{{(x-2)}^{2}}+{{(0-5)}^{2}}}\] \[{{(x+3)}^{2}}+16={{(x-2)}^{2}}+25\] \[{{x}^{2}}+9+3x+16={{x}^{2}}+4-4x+25\] \[7x=4\,\,\,\Rightarrow \,\,\,\,x=4/7\] Co-ordinate of  \[P(x,0)\] is \[(4/7,0)\]


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