Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
The mid points of the sides of triangle are $(1,5,-1)(0,4,-2)$ and $(2,3,4)$ then centroid of the triangle
MathematicsThree Dimensional GeometryKCETKCET 2021
Options:
  • A $(1,4,3)$
  • B $\left(1,4, \frac{1}{3}\right)$
  • C $(-1,4,3)$
  • D $\left(\frac{1}{3}, 2,4\right)$
Solution:
2095 Upvotes Verified Answer
The correct answer is: $\left(1,4, \frac{1}{3}\right)$
Given, mid points of the sides of triangle are $(1,5,-1),(0,4,-2)$ and $(2,3,4)$.
Let, $\left(x_{1}, y_{1}, z_{1}\right)=(1,5,=1)$,
$\left(x_{2}, y_{2}, z_{2}\right)=(0,4,-2) \text {, }$
$\left(x_{3}, y_{3}, z_{3}\right)=(2,3,4) \text {. }$
Then centroid of triangle, $G(x, y, z)=$
$\begin{aligned}
&\left(\frac{x_{1}+x_{2}+x_{3}}{3}, \frac{y_{1}+y_{2}+y_{3}}{3}, \frac{z_{1}+z_{2}+z_{3}}{3}\right) \\
&G(x, y, z)=\left(\frac{1+0+2}{3}, \frac{5+4+3}{3}, \frac{-1-2+4}{3}\right) \\
&=\left(1,4, \frac{1}{3}\right)
\end{aligned}$

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.