A triangle has corners at #(5 ,3 )#, #(9 ,7 )#, and #(6 ,5 )#. How far is the triangle's centroid from the origin?
1 Answer
Sep 27, 2016
Explanation:
If
#(x_1,y_1),(x_2,y_2)" and " (x_3,y_3)# are the vertices of a triangle then the coordinates of the#color(blue)"centroid"# are.
#x_c=1/3(x_1+x_2+x_3)" and " y_c=1/3(y_1+y_2+y_3)# That is the average of the coordinates of the vertices.
Using the given coordinates.
#x_c=1/3(5+9+6)=20/3" and " y_c=1/3(3+7+5)=5# coordinates of centroid are
#(20/3,5)# Since we are calculating the distance ( d) from the origin then, using
#color(blue)"Pythagoras' theorem"#
#d=sqrt((20/3)^2+5^2)=sqrt(400/9+25)#
#=sqrt(400/9+225/9)=sqrt(625/9)=25/3# distance from centroid to origin
#=25/3≈8.33" 2 d.p"#
