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).

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CBSE | Class 11 | Introduction to Three Dimensional Geometry | Maths | NCERT Exemplar

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:

It is given that:
Mid-points of sides of triangle $\mathrm{DEF}$ are:
$\mathrm{D}(1,2,-3), \mathrm{E}(3,0,1)$ and $\mathrm{F}(-1,1,-4)$
Using the geometry of centroid,
It is known that the centroid of triangle DEF is given as:
$\begin{aligned} \mathrm{G} =[(1+3-1) / 3,(2+0+1) / 3,(-3+1-4) / 3] \\ =(1,1,-2) \end{aligned}$
As a result, the centroid of triangle $\mathrm{DEF}$ is $(1,1,-2)$ .