Search any question & find its solution
Question:
Answered & Verified by Expert
If $A$ is $(2,5), B$ is $(4,-11)$ and $C$ lies on $9 x+7 y+4=0$, then the locus of the centroid of the $\triangle A B C$ is a straight line parallel to the straight line is
Options:
Solution:
2511 Upvotes
Verified Answer
The correct answer is:
$9 x+7 y+4=0$
According to question,
$x_1=\frac{2+4+x}{3} \Rightarrow x=3 x_1-6$
$\begin{aligned}
& y_1=\frac{5-11+y}{3} \Rightarrow y=3 y_1+6 \\
& \therefore 9\left(3 x_1-6\right)+7\left(3 y_1+6\right)+4=0
\end{aligned}$
Hence locus is $27 x+21 y-8=0$, which is parallel to $9 x+7 y+4=0$.
$x_1=\frac{2+4+x}{3} \Rightarrow x=3 x_1-6$
$\begin{aligned}
& y_1=\frac{5-11+y}{3} \Rightarrow y=3 y_1+6 \\
& \therefore 9\left(3 x_1-6\right)+7\left(3 y_1+6\right)+4=0
\end{aligned}$
Hence locus is $27 x+21 y-8=0$, which is parallel to $9 x+7 y+4=0$.
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.