A triangle has corners at #(3 ,4 )#, #(6 ,3 )#, and #(2 ,7 )#. How far is the triangle's centroid from the origin?
1 Answer
≈ 5.935 units
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 , thenx-coord
#(x_c) = 1/3(x_1+x_2+x_3)" and " #
y-coord# (y_c) = 1/3(y_1+y_2+y_3) # here
#x_c = 1/3(3+6+2) = 11/3" and " y_c = 1/3(4+3+7) = 14/3 # coords of centroid
# = (11/3 , 14/3 ) # To calculate the distance the centroid is from the origin use the
#color(blue)" distance formula " #
#d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2 )# where
#(x_1,y_1)" and " (x_2,y_2)" are 2 coord points "# The 2 points here are the centroid and the origin.
Since the origin is one of the points this simplifies the distance formula to :
#d = sqrt((11/3)^2 + (14/3)^2) = sqrt((121/9)+(196/9))#
# = sqrt(317/9) ≈ 5.935" units " #
