A triangle has corners at #(7 ,3 )#, #(4 ,4 )#, and #(6 ,7 )#. How far is the triangle's centroid from the origin?

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Answer 1 · 2018-02-16T06:09:48

Distance of centroid from origin is #vec(GO) ~~ color (green)(7.341)# units

Given the coordinates of the three vertices of the triangle.

#A(7,3), B(4,4), C(6,7)#

To find centroid G and it’s distance from origin.

#G(x,y) = (x1+ x2 + x3)/3, (y1 + y2 + y3)/3#

#G (x) = (7 + 4 + 6) / 3 = (17)/3#

#G(y) = (3 + 4 + 7) / 3 = (14)/3#

Distance centroid from origin can be arrived at by using distance formula

#d = sqrt((x2-x1)^2 + (y2-y1)^2)#

#vec(GO) = sqrt((17/3)^2 + (14/3)^2) # coordinates of origin is (0,0)

#vec(GO) ~~ color (green)(7.341)# units