Question

A triangle has corners at `(4 ,6 )`, `(3 ,9 )`, and `(2 ,5 )`. How far is the triangle's centroid from the origin?

Answer 1

The distance of the centroid from the origin is `=7.31`

Explanation:

Let the coordinates of the triangle be `(x_1,y_1),(x_2,y_2),(x_3,y_3)`

Then the centroid is given by `((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)`

So the coordinates of the centroid are `(9/3,20/3)`
Let coordinates of centroid be `(x_c,y_c)`

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

So the distance is `=sqrt(9+400/9)=sqrt(481/9)=7.31`