The lengths of the medians of a triangle $ ABC $ are:
$$ m_a = \frac{ 5 \sqrt{ 29}}{ 4 } ~~,~~ m_b = \sqrt{ 5 } ~~,~~ m_c = \frac{\sqrt{ 485 }}{ 4 } $$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(-\dfrac{ 13 }{ 2 },~-\dfrac{ 7 }{ 4 }\right) $.
The distance between $ A $ and $ M $ is:
$$ d(A,M) = \frac{ 5 \sqrt{ 29}}{ 4 } $$