A triangle has corners at #(1 ,9 )#, #(3 ,4 )#, and #(4 ,5 )#. How far is the triangle's centroid from the origin?
1 Answer
Sep 30, 2016
≈ 6.566 units.
Explanation:
Given
# (x_1,y_1),(x_2,y_2)" and " (x_3,y_3)# are the vertices of a triangle then the coordinates of the 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.
substituting the given coordinates into the above.
#x_c=1/3(1+3+4)=8/3" and " y_c=1/3(9+4+5)=6#
#rArr"coordinates of centroid" =(8/3,6)# To calculate the distance from this point to the origin use
#color(blue)"Pythagoras' theorem"#
#d=sqrt((8/3)^2+6^2)=sqrt(64/9+324/9)#
#=sqrt(388/9)≈6.566" to 3 decimal places"#
