If $\mathrm{G}(3,-5, \mathrm{r})$ is the centroid of $\triangle \mathrm{ABC}$, where $\mathrm{A} \equiv(7,-8…
If $\mathrm{G}(3,-5, \mathrm{r})$ is the centroid of $\triangle \mathrm{ABC}$, where $\mathrm{A} \equiv(7,-8,1)$, $B \equiv(p, q, 5), C \equiv(q+1,5 p, 0)$ are vertices of the triangle $A B C$, then the values of $p, q, r$ are respectively
-2,3,2
-4,5,4
6,5,4
2,-2,3
Solution
$\mathrm{A}(7,-8,1) ; \mathrm{B}(\mathrm{p}, \mathrm{q}, 5)$ and $\mathrm{C}(\mathrm{q}+1,5 \mathrm{p}, 0)$ are vertices of $\triangle \mathrm{ABC}$ having centroid $\mathrm{G}(3,-5, \mathrm{r})$
$\therefore 3=\frac{7+p+q+1}{3},-5=\frac{-8+q+5 p}{3}, r=\frac{1+5+0}{3}$
$\mathrm{r}=2$
Solving (1) and (2), we get $p=-2, q=3$
$\mathrm{r}=2$
Solving (1) and (2), we get $p=-2, q=3$