11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-4

  • question_answer The centroid of a triangle ABC is at the point\[\left( \mathbf{1},\mathbf{2},\mathbf{3} \right)\].If the coordinate of A and B are\[\left( \mathbf{3},-\mathbf{5},-\mathbf{7} \right)\]and\[\left( \mathbf{1},\mathbf{7},\mathbf{6} \right)\], respectively then co-ordinate of C.

    A) \[(-1,4,10)\]                   

    B) \[\left( 4,-1,10 \right)\]     

    C) \[\left( 10,-1,4 \right)\]                 

    D) \[\left( 1,4,10 \right)\]

    Correct Answer: A

    Solution :

    [a] Let \[C\equiv \left( x,y,z \right)\] According to question,             \[1=\frac{3+1+x}{3}\Rightarrow 4+x=3\Rightarrow x=-1\] \[\Rightarrow 2=\frac{-5+7+y}{3}\] \[\Rightarrow 2+y=6\Rightarrow y=4\And 3=~\frac{-7+6+z}{3}\] \[-1+z=9\text{ }z=10.\text{ }C\equiv \left( -1,4,10 \right)\] Hence, option [a]is correct.

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