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

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Answer 1 · 2017-07-07T10:37:00

The centroid will move by $= 28.3$ $=28.3$

The centroid of the triangle, $A = (1, 3)$ $A=(1,3)$ , $B = (4, - 2)$ $B=(4,-2)$ and $C = (- 8, 5)$ $C=(-8,5)$ is

$C_{c} = (\frac{1 + 4 - 8}{3}, \frac{3 - 2 + 5}{3})$ $C_c=((1+4-8)/3,(3-2+5)/3)$

$= (- 1, 2)$ $=(-1,2)$

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

Let the centroid be $C_c'$ after the dilatation

$vec(DC_c')=5vec(DC_c)$

$=5<-1-4,2+3>$

$=<-25,25>$

$C_c'=(-25,25)+(4,-3)$

$=(-21,22)$

The distance between the centroids is

$d=sqrt((-21+1)^2+(22-2)^2)$

$=sqrt((-20)^2+(20)^2)$

$=sqrt800$

$=28.3$

A triangle has corners at (1 ,3 )(1,3)(1 ,3 ), (4 ,-2 )(4,−2)(4 ,-2 ), and (-8 ,5 )(−8,5)(-8 ,5 ). If the triangle is dilated by a factor of 5 55 about point #(4 ,-3 ), how far will its centroid move?