Question

A triangle has corners at `(2 ,9 )`, `(4 ,2 )`, and `(5 ,1 )`. How far is the triangle's centroid from the origin?

Answer 1

THe distance of the centroid from the origin is `5.43`

Explanation:

If a triangle has corners `(x_1,y_1)`,`(x_2,y_2)` and `(x_3,y_3)`

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

Let's call the centroid `(x_G, y_G)`

Then the distance from the origin is `=sqrt(x_G^2+y_G^2)`

The centroid is at `((2+4+5)/3,(9+2+1)/3)=(11/3,4)`

So the distance `= sqrt(11^2/3^2+4^2)=5.43`