A triangle has corners at #(6 ,4 )#, #(7 ,5 )#, and #(1 ,2 )#. How far is the triangle's centroid from the origin?
1 Answer
Jun 26, 2016
5.935
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) = (6,4)#
#(x_2,y_2) = (7,5)#
#(x_3,y_3) = (1,2)#
The centroid coordinates are
#C = ((6+7+1)/3, (4+5+2)/3) => (14/3, 11/3)#
Distance from origin
#D = sqrt((14/3)^2+(11/3)^2)#
#=(sqrt (4.67^2+3.67^2))#
#= sqrt 35.222#
#=5.935#