Find the centroid of a triangle,

Given:

Mid-points of sides of triangle DEF are:

$\mathrm{D}(1,2,-3), \mathrm{E}(3,0,1)$ and $\mathrm{F}(-1,1,-4)$

By using the geometry of centroid,

We know that the centroid of triangle DEF is given as:

$\mathrm{G}=[(1+3-1) / 3,(2+0+1) / 3,(-3+1-4) / 3]$

$=(1,1,-2)$

Hence, the centroid of triangle DEF is $(1,1,-2)$.