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

1 Answer
Sep 26, 2017

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