A triangle has corners at #(2 ,4 )#, #(8 ,6 )#, and #(4 ,9 )#. How far is the triangle's centroid from the origin?
1 Answer
Mar 29, 2016
≈ 7.87 units
Explanation:
Given the vertices of a triangle A
#(x_1,y_1),B(x_2,y_2),C(x_3,y_3)# The centroid has coordinates :
# x_c = 1/3(x_1 + x_2 + x_3 ) : y_c = 1/3(y_1+y_2+y_3)# For the vertices given :
#x_c = 1/3(2+8+4) = 14/3" and " y_c = 1/3(4+6+9) = 19/3# the coordinates of the centroid
# = (14/3 , 19/3) # To calculate distance from origin use the
#color(blue)" distance formula " #
# d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)# since the origin has coordinates (0 , 0) the formula is simplified.
#rArr d = sqrt((14/3)^2 + (19/3)^2) #
# = sqrt(196/9 + 361/9) = sqrt(557/9) ≈ 7.87#
