The lengths of the medians of a triangle $ ABC $ are:
$$ m_a = \frac{\sqrt{ 905 }}{ 2 } ~~,~~ m_b = 4 \sqrt{ 5 } ~~,~~ m_c = \frac{ 5 \sqrt{ 17}}{ 2 } $$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(8,~\dfrac{ 3 }{ 2 }\right) $.
The distance between $ A $ and $ M $ is:
$$ d(A,M) = \frac{\sqrt{ 905 }}{ 2 } $$