Question

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

Answer 1

The distance is `=sqrt356/3`

Explanation:

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

Then the centroid is `(x_c,y_c)=((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)`

`:. x_c=(5+2+3)/3=10/3`

and `y_c=(5+7+4)/3=16/3`

The distance from the origin is `sqrt(x_c^2+y_c^2)`

`=sqrt(100/9+256/9)=sqrt356/3`