Question

A triangle has corners at `(7 ,6 )`, `(4 ,3 )`, and `(5 ,1 )`. How far is the triangle's centroid from the origin?

Answer 1

Triangle's centroid is `6.289` units away from the origin.

Explanation:

Centroid of a triangle, whose corners are `(x_1,y_1)`, `(x_2,y_2)` and `(x_3,y_3)`, is given by `(1/3(x_1+x_2+x_3),1/3(y_1+y_2+y_3))`

Hence centroid of the triangle whose corners are `(7,6)`, `(4.3)` and `(5,1)` is

`(1/3(7+4+5),1/3(6+3+1))` or `(16/3,10/3)`

And its distance from origin `(0,0)` is

`sqrt((16/3-0)^2+(10/3-0)^2)=sqrt(256/9+100/9)`

= `1/3sqrt356=1/3xx18.868=6.289`