Question:
Find the centroid of a triangle, the mid-point of whose sides are D (1, 2, – 3), E (3, 0, 1) and F (– 1, 1, – 4).
Solution:
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 $(1,1,-2)$.