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JEE Main & Advanced Mathematics Straight Line Question Bank Problems related to triangle and quadrilateral Locus

  • question_answer
    If A is (2, 5), B is (4, -11) and C lies on \[9x+7y+4=0\], then the locus of the centroid of the \[\Delta ABC\] is a straight line parallel to the straight line is                                                               [MP PET 1986]

    A) \[7x-9y+4=0\]                           

    B) \[9x-7y-4=0\]

    C) \[9x+7y+4=0\]                      

    D) \[7+9y+4=0\]

    Correct Answer: C

    Solution :

               According to question , \[{{x}_{1}}=\frac{2+4+x}{3}\Rightarrow x=3{{x}_{1}}-6\]                    \[{{y}_{1}}=\frac{5-11+y}{3}\Rightarrow y=3{{y}_{1}}+6\]                    \[\therefore \] \[9(3{{x}_{1}}-6)+7(3{{y}_{1}}+6)+4=0\]                    Hence locus is\[27x+21y-8=0\], which is parallel to 9x+7y+4 = 0.


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