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

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Answer 1 · 2017-07-03T06:47:29

The centroid will move by $=33.4$

The centroid of the triangle, $A=(2,3)$ , $B=(4,-1)$ and $C=(-8,6)$ is

$C_c=((2+4-8)/3,(3-1+6)/3)$

$=(-2/3,8/3)$

Let the point $D=(4,-3)$

Let the centroid be $C_c'$ after the dilatation

$vec(DC_c')=4vec(DC_c)$

$=5<-2/3-4,8/3+3>$

$=<-70/3,85/3>$

$C_c'=(-70/3,85/3)+(4,-3)$

$=(-58/3,74/3)$

The distance between the centroids is

$d=sqrt((-58/3+2/3)^2+(74/3+3)^2)$

$=sqrt((56/3)^2+(83/3)^2)$

$=(sqrt10025)/3$

$=33.4$

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