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

1 Answer
May 25, 2016

Triangle's centroid is 5.963 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), (4.4) and (3,1) is

(1/3(9+4+3),1/3(3+4+1)) or (16/3,9/3)

And its distance from origin (0,0) is

sqrt((16/3-0)^2+(8/3-0)^2)=sqrt(256/9+64/9)

= 1/3sqrt320=8/3xxsqrt5=8/3xx2.236=5.963