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
Explanation:
Centroid Formula is
#C = ((x_1+x_2+x_3)/3, (y_1+y_2+y_3)/3)# where
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
#D = sqrt((4)^2+(5)^2)#
#=sqrt (16+25)#
#= sqrt 41#