A triangle has corners at #(5 ,2 )#, #(4 ,6 )#, and #(3 ,5 )#. How far is the triangle's centroid from the origin?

1 Answer
May 9, 2016

≈ 5.897

Explanation:

The first step is to find the coordinates of the centroid.

If #(x_1,y_1),(x_2,y_2)" and " (x_3,y_3)#
are the coordinates of the vertices of a triangle , then

x-coord #(x_c)=1/3(x_1+x_2+x_3)" and "#

y-coord#(y_c)=1/3(y_1+y_2+y_3)#
so #x_c=1/3(5+4+3)=4" and " y_c=1/3(2+6+5)=13/3#

coords of centroid #=(4,13/3)#

To calculate the distance the centroid is 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 #(4,13/3)#

#d=sqrt((4-0)^2+(13/3-0)^2)=sqrt(16+169/9)#

#=sqrt(144/9+169/9)=sqrt(313/9) ≈ 5.897 #