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A triangle has corners at #(7 ,2 )#, #(6 ,7 )#, and #(3 ,1 )#. How far is the triangle's centroid from the origin?

Answer 1

Ella Armstrong

The distance is #=6.3#

The centroid is

#(x_c,y_c)=((x_1+x_1+x_3)/3,(y_1+y_2+y_3)/3)#

Therefore,

#(x_c,y_c)=((7+6+3)/3,(2+7+1)/3)=(16/3,10/3)#

The distance from the origin is

#d_C=sqrt((x_c)^2+(y_c)^2)#

#=sqrt((16/3)^2+(10/3)^2)#

#=sqrt356/3#

#=6.3#

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Answer 2

Sadie Allen

The centroid of a triangle can be found by taking the average of the coordinates of its vertices. In this case, the centroid is located at ((7+6+3)/3, (2+7+1)/3). Calculate the distance between this centroid and the origin using the distance formula, which is the square root of the sum of the squares of the coordinates.

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