Question

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

Answer 1

Distance of centroid from origin is (approximately) `6.15` units

Explanation:

The centroid of a triangle with corners at `(x_1,y_1), (x_2,y_2), and (x_3,y_3)` can be located using the formula
`color(white)("XXX")(x_c,y_c)=((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)`

In this case
`color(white)("XXX")(cx_c,y_c)=((9+2+3)/3,(3+5+4)/3)=(14/3,4)`

The distance of the centroid at `(14/3,4)` and the origin at `(0,0)`
can be calculated using the Pythagorean Theorem as
`color(white)("XXX")d=sqrt((14/3)^2+4^2) ~~6.15`