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JEE Main & Advanced Mathematics Rectangular Cartesian Coordinates Question Bank Points related to triangle (Orthocente Circumcentre Incentre), Area of some geometrical figures Collinearity

  • question_answer
    If the points \[(a,b),\,(a',b')\]and \[(a-a',b-b')\]are collinear, then      [RPET 1999]

    A) \[ab'=a'b\]

    B) \[ab=a'b'\]

    C) \[aa'=bb'\]

    D) \[{{a}^{2}}+{{b}^{2}}=1\]

    Correct Answer: A

    Solution :

    \[\frac{a-{a}'-{a}'}{{a}'-a}=\frac{b-{b}'-{b}'}{{b}'-b}\] \[\Rightarrow \,\,\,\frac{a-2{a}'}{{a}'-a}=\frac{b-2{b}'}{{b}'-b}\]\[\Rightarrow \,\,\frac{a}{{{a}'}}=\frac{b}{{{b}'}}\,\,\Rightarrow \,\,a{b}'={a}'b.\]


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