Question

A triangle has corners at `(1 ,6 )`, `(7 ,4 )`, and `(5 ,9 )`. How far is the triangle's centroid from the origin?

Answer 1

the centroid is `58.89` when 3 vertices of a triangle #(xunits away from the origin.

Explanation:

when 3 vertices of a triangle are `(x_1,y_1),(x_2,y_2),(x_3,y_3)` then the centroid of the triangle is `G=((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)`
substituting the values we get the centroid as `G=(13/3,19/3)`
the distance between `G(13/3,19/3) and C(0,0)` is `sqrt[(x_2-x_1)^2+(y_2-y_1)^2` substituting in the formula we get distance as `sqrt(530/9)~~58.89`