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

1 Answer
jags
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#

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