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"#