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
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
#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#