Question

A triangle has corners at `(4 ,3 )`, `(2 ,6 )`, and `(7 ,5 )`. How far is the triangle's centroid from the origin?

Answer 1

`sqrt365/3=6.37`

Explanation:

Centroid `(x_c,y_c)` of a triangle with given points `(x1,y1),(x2,y2) and (x3,y3)`:
`x_c= (x1+x2+x3)/3,`
`y_c= (y1+y2+y3)/3`,
where `x1,x2,x3,y1,y2,y3` are the coordinates of the vertices of the triangle.

Given : `A(4,3), B(2,6), C(7,5)`
Let `D(x,y)` be the centroid of the triangle,

`x=(4+2+7)/3=13/3`

`y=(3+6+5)/3=14/3`

The distance, `d`, from the origin is :

`d=sqrt((13/3)^2+(14/3)^2)=sqrt(365/9)=sqrt365/3=6.37`