A triangle has corners at $(-1 ,7 )$ , $(-5 ,-3 )$ , and $(2 ,9 )$ . If the triangle is dilated by a factor of $5$ about point #(-7 ,1 ), how far will its centroid move?

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Answer 1 · 2017-03-20T17:45:40

The distance is $=24$

Let $ABC$ be the triangle

$A=(-1,7)$

$B=(-5,-3)$

$C=(2,9)$

The centroid of triangle $ABC$ is

$C_c=((-1-5+2)/3,(7+(-3)+9)/3)=(4/3,13/3)$

Let $A'B'C'$ be the triangle after the dilatation

The center of dilatation is $D=(-7,1)$

$vec(DA')=5vec(DA)=5*<6,6> = <30,30>$

$A'=(30-7,30+1)=(23,31)$

$vec(DB')=5vec(DB)=5*<2,-4> = <10,-20>$

$B'=(10-7,-20+1)=(3,-19)$

$vec(DC')=5vec(DC)=5*<9,8> = <45,40>$

$C'=(45-7,40+1)=(38,41)$

The centroid $C_c'$ of triangle $A'B'C'$ is

$C_c'=((23+3+38)/3,(31-19+41)/3)=(64/3,53/3)$

The distance between the 2 centroids is

$C_cC_c'=sqrt((64/3-4/3)^2+(53/3-13/3)^2)$

$=1/3sqrt(60^2+40^2)=72.11/3=24$

A triangle has corners at (-1 ,7 )(-1 ,7 ), (-5 ,-3 )(-5 ,-3 ), and (2 ,9 )(2 ,9 ). If the triangle is dilated by a factor of 5 5 about point #(-7 ,1 ), how far will its centroid move?