A triangle has corners at $(-2 ,6 )$ , $(4 ,-3 )$ , and $(2 ,9 )$ . If the triangle is dilated by a factor of $5$ about point #(-5 ,6 ), how far will its centroid move?

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Answer 1 · 2017-06-20T19:51:35

The centroid will move by $=26.6$

The centroid of the triangle, $A=(-2,6)$ , $B=(4,-3)$ and $C=(2,9)$ is

$C_c=((-2+4+2)/3,(6-3+9)/3)$

$=(4/3,4)$

Let the point $D=(-5,6)$

Let the centroid be $C_c'$ after the dilatation

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

$=5<4/3+5,4-6>$

$=<95/3,-10>$

$C_c'=(95/3,-10)+(-5,6)$

$=(80/3,-4)$

The distance between the centroids is

$d=sqrt((80/3-4/3)^2+(-4-4)^2)$

$=sqrt((76/3)^2+(8)^2)$

$=sqrt(705.8)$

$=26.6$

A triangle has corners at (-2 ,6 )(-2 ,6 ), (4 ,-3 )(4 ,-3 ), and (2 ,9 )(2 ,9 ). If the triangle is dilated by a factor of 5 5 about point #(-5 ,6 ), how far will its centroid move?