A triangle has corners at #(5 ,2 )#, #(9 ,7 )#, and #(3 ,5 )#. How far is the triangle's centroid from the origin?
1 Answer
Explanation:
The first step here is to find the coordinates of the centroid using the following.
Given 3 vertices of a triangle
# (x_1,y_1),(x_2,y_2),(x_3,y_3)# x-coordinate
#(x_c)=1/3(x_1+x_2+x_3)# and y-coordinate
#(y_c)=1/3(y_1+y_2+y_3)# using the coordinates given in the question
#rArrx_c=1/3(5+9+3)=17/3# and
#y_c=1/3(2+7+5)=14/3# hence coordinates of centroid
#=(17/3,14/3)# To calculate the distance from the origin use the
#color(blue)" distance formula"#
#color(red)(|bar(ul(color(white)(a/a)color(black)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2))color(white)(a/a)|)))#
where#(x_1,y_1)" and " (x_2,y_2)" are 2 points"# The 2 points here are (0 ,0) and
#(17/3,14/3)#
#d=sqrt((17/3-0)^2+(14/3-0)^2)=sqrt((17/3)^2+(14/3)^2)#
#=sqrt(289/9+196/9)=1/3sqrt485≈7.34#
