Question

A triangle has corners at `(1 ,9 )`, `(5 ,4 )`, and `(6 ,2 )`. How far is the triangle's centroid from the origin?

Answer 1

`sqrt41` units

Explanation:

A triangle with vertices at `(x_1,y_1), (x_2,y_2) and (x_3,y_3)` has centroid at `((x_1+x_2+x_3)/3, (y_1+y_2+y_3)/3)`
`=>` centroid of the triangle `=((1+5+6)/3, (9+4+2)/3)=(4,5)`
Let `d` be the distance between the centroid and the origin `O(0,0)`,
`=> d=sqrt(4^2+5^2)=sqrt(16+25)=sqrt41` units