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

Question

1342 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-07T10:37:00

The centroid will move by $=28.3$

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

$C_c=((1+4-8)/3,(3-2+5)/3)$

$=(-1,2)$

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

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 ), (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?