If the origin is the centroid of the triangle whose vertices are $\mathrm{A}(2, \mathrm{p},-3)$,…

If the origin is the centroid of the triangle whose vertices are $\mathrm{A}(2, \mathrm{p},-3)$, $\mathrm{B}(\mathrm{q},-2,5)$ and $\mathrm{C}(-5,1, \mathrm{r})$, then
  1. $p=-1, \quad q=3, \quad r=-2$
  2. $p=1, \quad q=-3, \quad r=-2$
  3. $p=1, \quad q=3, \quad r=2$
  4. $p=1, \quad q=3, \quad r=-2$

Solution

Origin is centroid of $\Delta \mathrm{ABC}$. $\begin{array}{l} \therefore \frac{2+q-5}{3}=0 \Rightarrow-3+q=0 \Rightarrow q=3 \\ \therefore \frac{p-2+1}{3}=0 \Rightarrow p-1=0 \Rightarrow p=1 \\ \therefore \frac{-3+5+r}{3}=0 \Rightarrow 2+r=0 \Rightarrow r=-2 \end{array}$

Asked in: MHT CET 2020 (15 Oct Shift 1)

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