Question

A triangle has corners at `(3 ,4 )`, `(6 ,3 )`, and `(2 ,8 )`. How far is the triangle's centroid from the origin?

Answer 1

See below.

Explanation:

The centroid of a triangle is the average of the vertices of that triangle, or:

`((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)`

So,

`((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)=((3+6+2)/3,(4+3+8)/3)=((11)/3,(15)/3)=(11/3,5)`

The distance from the origin is just `\sqrt((11/3)^2+5^2)=\sqrt(346)/3`