A triangle has corners at #(-2 ,3 )#, #(3 ,6 )#, and #(8 ,-6 )#. If the triangle is dilated by a factor of #2 # about point #(1 ,2 ), how far will its centroid move?

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Answer 1 · 2016-03-13T10:03:07

The new centroid #(5, 0)#

Compute centroid of the original triangle with corners #P_1(-2, 3)# and
#P_2(3, 6)# and #P_3(8, -6)# with reference point #(1, 2)#

#barx=(x_1+x_2+x_3)/3=(-2+3+8)/3=3#

#bary=(y_1+y_2+y_3)/3=(3+6-6)/3=1#

Compute centroid of the new triangle #(x, y)# using ratio #2:1#

#(x-1)/(3-1)=2/1#

#x-1=2*2#

#x=5#

#(y-2)/(1-2)=2/1#

#y-2=-1*2#

#y=0#

The new centroid #(5, 0)#

God bless....I hope the explanation is useful.