Question

A triangle has corners at `(7 ,9 )`, `(1 ,4 )`, and `(3 ,8 )`. How far is the triangle's centroid from the origin?

Answer 1

Triangle's centroid from the origin is `7.902` units away.

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 `(7,9)`, `(1.4)` and `(3,8)` is

`(1/3(7+1+3),1/3(9+4+8))` or `(11/3,21/3)`

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

`sqrt((11/3-0)^2+(21/3-0)^2)=sqrt(121/9+441/9)`

= `1/3sqrt562=1/3xx23.706=7.902`