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?

The centroid of a triangle lies on the median AM and divides it in a 2 to 1 ratio from the vertex, meaning the distance from A to the centroid is 6 and the distance from the centroid to M is 3. Because the total length of AM is 9 and MN is 1, point N lies between the centroid and M, making its distance from M equal to 1. The distance from N to the centroid is the distance from the centroid to M minus MN, which is 3 - 1 = 2.

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