A triangle has corners at (6 ,4 ), (7 ,5 ), and (1 ,2 ). How far is the triangle's centroid from the origin?

1 Answer
Jun 26, 2016

5.935

Explanation:

Centroid Formula is

C = ((x_1+x_2+x_3)/3, (y_1+y_2+y_3)/3) where

x_1, x_2, x_3 are the x-coordinates of the vertices of the triangle.
y_1, y_2, y_3 are the y-coordinate’s of the vertices of the triangle.

In our triangle,

(x_1, y_1) = (6,4)

(x_2,y_2) = (7,5)

(x_3,y_3) = (1,2)

The centroid coordinates are

C = ((6+7+1)/3, (4+5+2)/3) => (14/3, 11/3)

Distance from origin (0,0) to C(14/3, 11/3) using the distance formula is

D = sqrt((14/3)^2+(11/3)^2)

=(sqrt (4.67^2+3.67^2))

= sqrt 35.222

=5.935