A triangle has corners at $(2 ,3 )$ , $(1 ,-2 )$ , and $(-6 ,6 )$ . 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 · 2017-05-09T07:02:44

The centroid will move by $=33.9$

Let $ABC$ be the triangle

$A=(2,3)$

$B=(1,-2)$

$C=(-6,6)$

The centroid of triangle $ABC$ is

$C_c=((2+1-6)/3,(3-2+6)/3)=(-3/3,7/3)=(-1,7/3)$

Let the new centroid after the dilatation be $C_c'$

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

Then,

$vec(DC_c')=5vec(DC_c)=5(-1-4,7/3+3)=(-25,80/3)$

$C_c'=(-25,80/3)+(4,3)=(-21,89/3)$

Therefore,

the distance $C_cC_c'$

$=sqrt((-21+1)^2+(89/3-7/3)^2)$

$=sqrt(400+747.1)$

$=33.9$

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