The length of a median of a triangle is 36 units. Describe
the location of the centroid on that median.
All you can say is that the centroid is on the median.
http://www.mathopenref.com/trianglecentroid.html
The centroid divides the median in the ratio of 2:1, with the longer part towards the vertex.
So your 36 unit median is divided into length of 24 and 12 by the centroid.
To describe the location of the centroid on a median of a triangle, we need to understand what a centroid is.
The centroid of a triangle is the point where all three medians intersect. A median is a line segment drawn from a vertex of the triangle to the midpoint of the opposite side.
Now, in this case, you already know the length of the median is 36 units. To describe the location of the centroid on that median, we need to understand the relationship between the centroid and the median.
The centroid of a triangle divides each median into two parts. The length of the segment from the centroid to the vertex is twice as long as the length from the centroid to the midpoint of the opposite side.
So, if the length of the median is 36 units, the distance from the centroid to the vertex will be twice as long, which is 2 * 36 = 72 units.
Therefore, the location of the centroid on that median will be 72 units away from the vertex of the triangle, along the median segment. To be more precise, it will be located closer to the vertex since the segment towards the centroid is twice as long as the segment towards the midpoint of the opposite side.