Question

A triangle has corners at `(9 ,5 )`, `(2 ,7 )`, and `(3 ,4 )`. How far is the triangle's centroid from the origin?

Answer 1

`2/3sqrt103`

Explanation:

a triangle with vertices at `(x_1,y_1), (x_2,y_2), (x_3,y_3)` has centroid at `((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)`

A triangle has corners at (9,5), (2,7) and (3,4)

Hence centroid is `((9+2+3)/3, (5+7+4)/3)`
or `(14/3,16/3)`

distance between centroid`(14/3,16/3)` and origin `(0,0)`
distance formula `d=sqrt((x_2-x_1)^2+(y_2-y_1)^2`
`d=sqrt((14/3-0)^2+(16/3-0)^2`
`d=sqrt(196/9+216/9)=sqrt(412/9)=2/3sqrt103`