Q210 / 270 · NDA 2017 (Phase 1) · Mathematics

If the centroid of a triangle formed by $(7, x),(y,-6)$ and $(9,10)$ is $(6,3)$, then the values of $x$ and $y$ are respectively

  • Correct answer
    A
    5,2
  • B
    2,5
  • C
    1,0
  • D
    0,0

Solution

Centroid of given triangle $\begin{aligned} & =\left(\frac{7+y+9}{3}, \frac{x-6+10}{3}\right) \\ & \Rightarrow\left(\frac{16+y}{3}, \frac{x+4}{3}\right)=(6,3) \\ & \Rightarrow 16+y=18 ; x+4=9 \\ & \Rightarrow y=2 ; x=5 \end{aligned}$

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

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