# find the lengths of the medians of a triangle whose mid points of vertices are  (3,5),(5,3)and(7,7)  { simple method}

$\triangle DEF$ is similar to $\triangle ABC$ and is contracted by a factor of ½ (by BPT). So it suffices to find the medians of $\triangle DEF$ and double them. This way AD = 6 = BE and CF = $2 \sqrt 3$ are readily obtained