Search any question & find its solution
Question:
Answered & Verified by Expert
If the origin is the centroid of a triangle $A B C$ having vertices $A(a, 1,3), B(-2, b,-5)$ and $C(4,7, c)$, find the values of $\mathrm{a}, \mathrm{b}, \mathrm{c}$.
Solution:
1446 Upvotes
Verified Answer
Here, $(0,0,0) \equiv\left(\frac{\mathrm{a}-2+4}{3}, \frac{1+\mathrm{b}+7}{3}, \frac{3-5+\mathrm{c}}{3}\right)$
On Equating
$$
\begin{aligned}
&\frac{\mathrm{a}+2}{3}=0, \frac{\mathrm{b}+8}{3}=0, \frac{\mathrm{c}-2}{3}=0 \\
&\Rightarrow \mathrm{a}=-2, \mathrm{~b}=-8, \mathrm{c}=2
\end{aligned}
$$
On Equating
$$
\begin{aligned}
&\frac{\mathrm{a}+2}{3}=0, \frac{\mathrm{b}+8}{3}=0, \frac{\mathrm{c}-2}{3}=0 \\
&\Rightarrow \mathrm{a}=-2, \mathrm{~b}=-8, \mathrm{c}=2
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.