The lengths of the medians of a triangle $ ABC $ are:
$$ m_a = \frac{\sqrt{ 61 }}{ 2 } ~~,~~ m_b = \frac{\sqrt{ 37 }}{ 2 } ~~,~~ m_c = 2 $$A median $ m_a $ is a line segment joining a vertex $ A $ to the midpoint of the side $ BC $. In this example the midpoint of $ BC $ is $ \left(2,~\dfrac{ 9 }{ 2 }\right) $.
The distance between $ A $ and $ M $ is:
$$ d(A,M) = \frac{\sqrt{ 61 }}{ 2 } $$