Q178 / 270 · NDA 2016 (Phase 1) · Mathematics

Consider the lines $y=3 x, y=6 x$ and $y=9$. The centroid of the triangle is at which one of the following points?

  • A
    $(3,6)$
  • Correct answer
    B
    $\left(\frac{3}{2}, 6\right)$
  • C
    $(3,3)$
  • D
    $\left(\frac{3}{2}, 9\right)$

Solution

Coordinates of $O, A, B$ are $(0,0)\left(\frac{3}{2}, 9\right),(3,9)$ respectively. $\therefore$ Centroid $C=\left[\left(\frac{0+\frac{3}{2}+3}{3}\right),\left(\frac{0+9+9}{3}\right)\right]=\left(\frac{3}{2}, 6\right)$

Hence, the correct answer is option: 'B'.

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