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

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Answer 1 · 2017-05-12T15:27:28

The centroid will move by $=sqrt68/3=2.75$

The centroid of the triangle, $A=(5,2)$ , $B=(-3,-3)$ and $C=(1,-2)$ is

$C_c=((5-3+1)/3,(2-3-2)/3)$

$=(1,-1)$

Let the point $D=(5,-2)$

Let the centroid be $C_c'$ after the dilatation

$vec(DC_c')=1/3vec(DC_c)$

$=1/3<1-5,-1+2>$

$=<-4/3,1/3>$

$C_c'=(-4/3,1/3)+(5,-2)$

$=(11/3,-5/3)$

The distance between the centroids is

$d=sqrt((11/3-1)^2+(-5/3+1)^2)$

$=sqrt(64/9+4/9)$

$=sqrt68/3$

$=2.75$

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