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SSC Sample Paper Mock Test-18 SSC CGL Tear-II Paper-1

  • question_answer
    If two vertices of a triangle are \[(-2,3)\]and \[(5,-1),\] orthocenter lies at the origin and centroid on the line \[x+y=7,\] then the third vertex lies at

    A) (7, 4)

    B)  (8, 14)

    C)  (12, 21)

    D)  None of these

    Correct Answer: D

    Solution :

    Given, O (0, 0) is the orthocenter. Let A (h, k) be the third vertex, B\[(-\,\,2,3),\]and C\[(5,-1)\]the other two vertices. Then the slope of the line through A and O is k / h, while the lines through B and C has the slope \[-\,\,4/7.\] By the property of the orthocenter, these two lines must be perpendicular, so we have
    \[(\text{k/h})\left( -\frac{4}{7} \right)=-1\]\[\Rightarrow \]\[\text{k/h}=\frac{7}{4}\]  ?(i)
    Also,     \[\frac{5-2+h}{3}+\frac{-1+3+k}{3}=7\]
    \[\Rightarrow \]               \[h+k=16\]                    ?(ii)
    Which is not satisfied by the points given in ,  or .


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