A triangle has corners at #(2 ,4 )#, #(7 ,6 )#, and #(4 ,9 )#. How far is the triangle's centroid from the origin?

Answer 1

#= 7.67#

Centroid Formula is

#C = ((x_1+x_2+x_3)/3, (y_1+y_2+y_3)/3)# where

#x_1#, #x_2#, #x_3# are the #x#-coordinates of the vertices of the triangle. #y_1#, #y_2#, #y_3# are the #y#-coordinate’s of the vertices of the triangle.

In our triangle,

#(x_1, y_1) = (2,4)#

#(x_2,y_2) = (7,6)#

#(x_3,y_3) = (4,9)#

The centroid coordinates are

#C = ((2+7+4)/3, (4+6+9)/3) => (13/3, 19/3)#

Distance from origin #(0,0)# to #C(13/3, 19/3)# using the distance formula is

#D = sqrt((13/3)^2+(19/3)^2)#

#D = sqrt((4.33)^2+(6.33)^2)#

#=sqrt (18.78 + 40.11)#

#= sqrt 58.89#

#= 7.67#

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Answer 2

Theodore Abad

The centroid of the triangle with vertices at (2, 4), (7, 6), and (4, 9) is located at the point (4.33, 6.33). The distance from this centroid to the origin can be calculated using the distance formula, which gives approximately 7.30 units.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.