A triangle has corners at (1 ,9 ), (5 ,4 ), and (3 ,8 ). How far is the triangle's centroid from the origin?

1 Answer
Jun 18, 2016

It is 7.61.

Explanation:

If (A_x, A_y), (B_x, B_y), (C_x, C_y) are the vertex of a triangle, the coordinates of the centroid are

CO_x=(A_x+B_x+C+x)/3

CO_y=(A_y+B_y+C+y)/3

In our case

CO_x=(1+5+3)/3=9/3=3

CO_y=(9+4+8)/3=21/3=7

Then the centroid has coordinates (3, 7) and its distance from the origin is simply

d=sqrt(3^2+7^2)=sqrt(9+49)=sqrt(58)\approx7.61.

enter image source here