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

1 Answer
Jun 27, 2016

= sqrt 41

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) = (1,4)

(x_2,y_2) = (7,6)

(x_3,y_3) = (4,5)

The centroid coordinates are

C = ((1+7+4)/3, (4+6+5)/3) => (12/3, 15/3) => (4,5)

Distance from origin (0,0) to C(4, 5) using the distance formula is

D = sqrt((4)^2+(5)^2)

=sqrt (16+25)

= sqrt 41