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JEE Main & Advanced JEE Main Paper (Held on 12-4-2019 Afternoon)

  • question_answer
    A triangle has a vertex at (1, 2) and the mid points of the two sides through it are (-1, 1) and (2, 3). Then the centroid of this triangle is: [JEE Main 12-4-2019 Afternoon]

    A) \[\left( \frac{1}{3},1 \right)\]               

    B) \[\left( \frac{1}{3},2 \right)\]

    C) \[\left( 1,\frac{7}{3} \right)\]               

    D) \[\left( \frac{1}{3},\frac{5}{3} \right)\]

    Correct Answer: B

    Solution :

    Let \[B(\alpha ,\beta )\]and \[C(\gamma ,\delta )\]             \[\frac{\alpha +1}{2}=-1\Rightarrow \alpha =-3\]             \[\frac{\beta +2}{2}=1\Rightarrow \beta =0\]\[\Rightarrow B\left( -3,0 \right)\] Now\[\frac{\gamma +1}{2}=2\Rightarrow \gamma =3\] \[\frac{\delta +2}{2}=3\Rightarrow \delta =4\]\[\Rightarrow C(3,4)\] \[\Rightarrow \]centroid of triangle is\[G\left( \frac{1}{3},2 \right)\]


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