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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 \[A(3,\text{ }4),\,B(7,\text{ }7),\,C(a,\text{ }b)\] be collinear and \[AC=10\], then \[(a,\text{ }b)\]=   

    A) \[(11,\text{ }10)\]

    B) \[(10,\text{ }11)\]

    C) \[(11/2,\,5)\]

    D) \[(5,\text{ }11/2)\]

    Correct Answer: A

    Solution :

    \[{{(a-3)}^{2}}+{{(b-4)}^{2}}=100\] and \[\frac{b-7}{3}=\frac{a-7}{4}\] Hence (a, b)=(11, 10). Trick: Check with options. We find that the point (11, 10) satisfies both the conditions i.e. \[AC=\sqrt{{{(11-3)}^{2}}+{{(10-4)}^{2}}}=10\]. Also this is collinear with A, B.


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