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

1 Answer
jags
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#

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