Question

A triangle has corners at `(7 ,6 )`, `(4 ,3 )`, and `(5 ,2 )`. How far is the triangle's centroid from the origin?

Answer 1

See below

Explanation:

To find the centroid of a triangle, we just find the average of the `x`-vertices, and then the average of the `y`-vertices, or `x_(centroid)=frac(x_1+x_2+x_3)(3)`
`y_(centroid)=frac(y_1+y_2+y_3)(3)`

The centroid is just:

`x_(centroid)=frac(7+4+5)(3)=frac(16)(3)` and
`y_(centroid)=frac(6+3+2)(3)=frac(11)(3)`

Then, the distance from the origin to this point is:

distance `=sqrt((frac(16)(3))^2+(frac(11)(3))^2)=sqrt(frac(377)(9))=frac(sqrt(377))(3)`