A triangle has corners at #(7 ,6 )#, #(8 ,2 )#, and #(5 ,9 )#. How far is the triangle's centroid from the origin?
1 Answer
Oct 8, 2016
Explanation:
The first step is to establish the position of the centroid.
Given
#(x_1,y_1),(x_2,y_2)" and " (x_3,y_3)# are the vertices of a triangle, then.
#x_c=1/3(x_1+x_2+x_3)# and
#y_c=1/3(y_1+y_2+y_3)#
#rArrx_c=1/3(7+8+5)=20/3# and
#y_c=1/3(6+2+9)=17/3#
#rArr" coordinates of centroid " =(20/3,17/3)# To calculate the distance (d) from the origin to the centroid, use
#color(blue)"Pythagoras' theorem"#
#d=sqrt((20/3)^2+(17/3)^2)=sqrt((400/9)+(289/9))#
#=sqrt(689/9)≈8.75" to 2 decimal places"#
