posted by JJ .
The length of a median of a triangle is 36 units. How many units from the vertex is the median?
Your question does not make sense as worded. The median PASSES THROUGH the vertex, so there is no distance between them.
The median is a line from a vertex to the midpoint of the opposite side. All triangles have three medians. They intersect at one point, called the centroid.
What you or your teacher may be really asking is how far from the vertex is from the CENTROID (sometimes called "median point").
There is a theorem that says that the centroid is 2/3 of the length of the median from the vertex. That would make the answer to your question 24 units.