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9th Class Mathematics Coordinate Geometry Question Bank Co-ordinate Geometry

  • question_answer
    What is the centroid of \[\Delta \mathbf{ABC}\] whose vertices, are \[\mathbf{A}\left( \mathbf{2},-\mathbf{4} \right),\] \[\mathbf{B}\left( -\mathbf{4},-\mathbf{2} \right)\] and \[\mathbf{C}\left( -1,\text{ }\mathbf{3} \right).\]

    A)  \[\left( -1,-1 \right)\]       

    B)  \[\left( -2,-2 \right)\]         

    C)  \[\left( 3,\text{ }4 \right)\]           

    D)  \[\left( 4,\text{ }4 \right)\]

    Correct Answer: A

    Solution :

    (a): Centroid of \[\Delta ABC=\left( \frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}}{3},\frac{{{y}_{1}}+{{y}_{2}}+{{y}_{3}}}{3} \right)\] \[=\left( \frac{2-4~-1}{3},\frac{-4-2+3}{3} \right)=(-1,-1)\] Hence, \[\left( -1,\text{ }1 \right)\] is the centroid of \[\Delta ABC\]   


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