Question

A triangle has corners at `(1 ,2 )`, `(9 ,6 )`, and `(8 ,5 )`. How far is the triangle's centroid from the origin?

Answer 1

The distance is `=7.4`

Explanation:

The centroid of a triangle `(x_g, y_g)`
is given by `x_g=(x_1+x_2+x_3)/3`
and `y_g=(y_1+y_2+y_3)/3`

Therefore `x_g=(1+9+8)/3=6`
and `y_g=(2+6+5)/3=13/3`

The distance from the origin `=sqrt (x_g^2+y_g^2)=sqrt(36+169/9)`
`=sqrt493/3=22.2/3=7.4`