Question

In $\Delta ABC,M$ is the mid point of $BC$. Length of $AM$ is $9,N$ is a point on $AM$ such that $MN=1$. What is the distance of $N$ from the centroid of the triangle?

• A. $2$
• B. $3$
• C. $5$
• D. $7$

Answer 1

The correct option is A $2$

$M$ is the mid point of $BC$.
$\Rightarrow AM$ is the median of $\Delta ABC$,
$G$ is the centroid of $\Delta ABC$.
$\Rightarrow G$ divides $AM$ in the ratio $2:1$

$\Rightarrow AG:GM=2:1$
Given, $AM=9$

Let $AG=x$

Then $GM=(9-x)$
$x:(9-x)=2:1$

$\Rightarrow \frac{x}{9-x}=\frac{2}{1}$

$\Rightarrow x=2(9-x)$
$\Rightarrow x=18-2x$

$\Rightarrow 3x=18$

$\Rightarrow x=6$

$\therefore GM=9-6=3$
Now, $GN=GM-NM=3-1=2$