Centroid of Tetrahedron (1 Viewer)

[Bob99]

How can I find the coordinates of the centroid (centre) of a tetrahedron, given that I know the coordinates of all the vertices.
I am aware of a method where you just calculate the average of all the points, however I want to solve it via vector methods.

 

[cossine]

How can I find the coordinates of the centroid (centre) of a tetrahedron, given that I know the coordinates of all the vertices.
I am aware of a method where you just calculate the average of all the points, however I want to solve it via vector methods.

So take the average of the vectors as per the definition.

 

[Bob99]

So take the average of the vectors as per the definition.

View attachment 38091

Yeah but the question im doing requires me to find it via vector methods. It's provided me with coordinates of the 4 vertices
<1,0,0>
<0,1,0>
<0,0,1>
<1,1,1>

 

[Bob99]

Ok I think I have figured it out, thanks for your help @cossine .

 

[Bob99]

Is it (1/2, 1/2, 1/2)?

yeah

 

[Bob99]

Oh ok, I just did it with vector equations and found the intersection point

did you use midpoints by any chance?
If you didnt, could you please show me your working out!!!!