A triangle has corners at (2 ,4 ), (7 ,6 ), and (4 ,9 ). How far is the triangle's centroid from the origin?

1 Answer
Jun 27, 2016

= 7.67

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) = (2,4)

(x_2,y_2) = (7,6)

(x_3,y_3) = (4,9)

The centroid coordinates are

C = ((2+7+4)/3, (4+6+9)/3) => (13/3, 19/3)

Distance from origin (0,0) to C(13/3, 19/3) using the distance formula is

D = sqrt((13/3)^2+(19/3)^2)

D = sqrt((4.33)^2+(6.33)^2)

=sqrt (18.78 + 40.11)

= sqrt 58.89

= 7.67