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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 distance of the middle point of the line joining the points \[(a\sin \theta ,0)\]and \[(0,a\cos \theta )\]from the origin is    [MP PET 1999]

    A) \[\frac{a}{2}\]

    B) \[\frac{1}{2}a(\sin \theta +\cos \theta )\]

    C) \[a(\sin \theta +\cos \theta )\]

    D) \[a\]

    Correct Answer: A

    Solution :

    Mid-point will be \[\left( \frac{a\,\sin \theta }{2},\,\frac{a\,\cos \theta }{2} \right)\] and distance from origin will be \[\sqrt{{{\left( \frac{a\,\sin \theta }{2}-0 \right)}^{2}}+{{\left( \frac{a\,\cos \theta }{2}-0 \right)}^{2}}}=\frac{a}{2}\].


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