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

  • question_answer
    The angle subtended by joining points \[A(3,0)\] and \[B(0,-2)\] to the origin point is:

    A) \[45{}^\circ \]

    B) \[90{}^\circ \]

    C) \[60{}^\circ \]

    D) \[30{}^\circ \]

    Correct Answer: B

    Solution :

    [b] Let \[O\equiv (0,0)\] be the origin.
    \[\therefore \,\,\,\,\,\,\,\,\,\,\,OA=\sqrt{{{(3-0)}^{2}}+{{(0-0)}^{2}}}=3\]
    \[OB=\sqrt{{{(0-0)}^{2}}+{{(0+2)}^{2}}}=2\]
    and \[AB=\sqrt{{{(3-0)}^{2}}+{{(0+2)}^{2}}}=\sqrt{9+4}=\sqrt{13}\]
    \[A{{B}^{2}}=O{{A}^{2}}+O{{B}^{2}}\]
    \[\therefore \] AB subtend right angle at origin.


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