Question

A triangle has corners at `(2 ,4 )`, `(8 ,6 )`, and `(7 ,1 )`. How far is the triangle's centroid from the origin?

Answer 1

The distance is`=sqrt410/3`

Explanation:

Let the corners of a triangle be `(x_1,y_1),(x_2,y_2) and(x_3,y_3)`

And the centrid `(x_c, y_c)`

Then `x_c=(x_1+x_2+x_3)/3=(2+8+7)/3=17/3`

`y_c=(y_1+y_2+y_3)/3=(4+6+1)/3=11/3`

The distance of the centroid from the origin is
`d=sqrt(x_c^2+y_c^2)=sqrt((17/3)^2+(11/3)^2)=sqrt410/3`