A triangle has corners at #(1 ,9 )#, #(7 ,8 )#, and #(4 ,5 )#. How far is the triangle's centroid from the origin?

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Answer 1 · 2018-06-05T20:40:20

#color(blue)((2sqrt(697))/3 " units")#

The centroid can be found by taking the arithmetic mean of the #bbx# and #bby# coordinates of the triangles vertices:

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

So we have:

#((1+7+4)/3,(9+8+5)/3)=>(4,22/3)#

Distance from the origin can be found using the distance formula:

#|d|=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#|d|=sqrt((4-0)^2+(22/3-0)^2)=(2sqrt(697))/3# units