Question

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

Answer 1

Triangle's centroid is `6.6` units away from the origin.

Explanation:

Centroid of a triangle, whose corners are `(x_1,y_1)`, `(x_2,y_2)` and `(x_3,y_3)`, is given by `(1/3(x_1+x_2+x_3),1/3(y_1+y_2+y_3))`

Hence centroid of the triangle whose corners are `(9,3)`, `(2.7)` and `(3,4)` is

`(1/3(9+2+3),1/3(3+7+4))` or `(14/3,14/3)`

And its distance from origin `(0,0)` is

`sqrt((14/3-0)^2+(14/3-0)^2))=sqrt((14/3)^2+(14/3)^2)`

= `14/3xxsqrt2=14/3xx1.4142=6.6`