A triangle has corners at #(6 ,7 )#, #(2 ,6 )#, and #(1 ,2 )#. How far is the triangle's centroid from the origin?

1 Answer
Jun 20, 2016

≈ 5.83 units

Explanation:

The first step here is to calculate the coordinates of the centroid.

Given 3 vertices #(x_1,y_1),(x_2,y_2),(x_3,y_3)# then the coordinates of the centroid are found as follows.

x-coordinate #x_c=color(red)(|bar(ul(color(white)(a/a)color(black)(1/3(x_1+x_2+x_3))color(white)(a/a)|)))#

and y-coordinate #y_c=color(red)(|bar(ul(color(white)(a/a)color(black)(1/3(y_1+y_2+y_3))color(white)(a/a)|)))#

Using the 3 vertices given here.

#x_c=1/3(6+2+1)=1/3xx9=3#

and #y_c=1/3(7+6+2)=1/3xx15=5#

Hence coordinates of centroid = (3 ,5)

To calculate the distance between (3 ,5) and (0 ,0) use #color(blue)"Pythagoras' theorem"#

#d=sqrt(3^2+5^2)=sqrt(9+25)=sqrt34≈5.83" units"#