A triangle has corners at #(6 ,6 )#, #(7 ,4 )#, and #(5 ,2 )#. How far is the triangle's centroid from the origin?
1 Answer
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) = (6,6)#
#(x_2,y_2) = (7,4)#
#(x_3,y_3) = (5,2)#
The centroid coordinates are
#C = ((6+7+5)/3, (6+4+2)/3) => (18/3, 12/3) => (6,4)#
Distance from origin
#D = sqrt(6^2+4^2)#
#=sqrt (36+16)#
#= sqrt 52#