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A triangle has corners at #(8 ,3 )#, #(4 ,-6 )#, and #(-2 ,5 )#. If the triangle is dilated by a factor of #5 # about point #(1 ,-3 ), how far will its centroid move?

Answer 1

Claire Akin

# 4/3sqrt{170}#

The centroid of the triangle is originally at

#({8+4+(-2)}/3,{3+(-6)+5}/3)=(10/3,2/3)#

The distance of the centroid from #(1,-3)# is

# sqrt{(10/3-1)^2+(2/3-(-3))^2}=1/3sqrt{7^2+11^2}=1/3sqrt{170}#

This distance is multiplied by a factor of 5 by the dilatation. The distance the centroid will move is #4 xx 1/3 sqrt{170} = 4/3sqrt{170}#

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Answer 2

Carson Arnold

The centroid of a triangle moves according to the same dilation factor as the vertices. Therefore, if the triangle is dilated by a factor of 5 about a point, the centroid will move five times as far from that point as the vertices do. Thus, the centroid will move 5 times the distance that the vertices move during the dilation.

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Answer from HIX Tutor

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