Q76 / 150 · MHT CET 2021 (22 Sep Shift 2) · Mathematics

If $\mathrm{G}(4,3,3)$ is the centroid of the triangle $\mathrm{ABC}$ whose vertices are $\mathrm{A}(\mathrm{a}, 3,1), \mathrm{B}(4,5, \mathrm{~b})$ and $\mathrm{C}(6, \mathrm{c}, 5)$, then the value of $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are

  • A
    $a=1, b=2, c=3$
  • B
    $a=3, b=2, c=1$
  • C
    $a=2, b=1, c=3$
  • Correct answer
    D
    $\mathrm{a}=2, \mathrm{~b}=3, \mathrm{c}=1$

Solution

We have vertices $\mathrm{A}(\mathrm{a}, 3,1) ; \mathrm{B}(4,5, \mathrm{~b}) ; \mathrm{C}(6, \mathrm{c}, 5)$ and $\mathrm{G}(4,3,3)$ of $\triangle \mathrm{ABC}$ $$ \frac{\mathrm{a}+4+6}{3}=4, \frac{3+5+\mathrm{c}}{3}=3, \frac{1+\mathrm{b}+5}{3}=3 \Rightarrow \mathrm{a}=2, \mathrm{c}=1, \mathrm{~b}=3 $$

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

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