A triangle has corners at #(9 ,1 )#, #(2 ,7 )#, and #(5 ,8 )#. How far is the triangle's centroid from the origin?
1 Answer
Jul 3, 2016
#=16/3sqrt (2)#
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) = (9,1)#
#(x_2,y_2) = (2,7)#
#(x_3,y_3) = (5,8)#
The centroid coordinates are
#C = ((9+2+5)/3, (1+7+8)/3) => (16/3, 16/3)#
Distance from origin
#D = sqrt((16/3)^2+(16/3)^2)#
#=16/3sqrt (2)#